If we are given a, b and A and b is equal to a then the triangle is isosceles so we can find the other two angles without using the Sine Rule. To cover the answer again, click "Refresh" ("Reload"). Therefore, b sin A = 2 /2 = , which is equal to a. Because $$\theta$$ is obtuse, the terminal side of the angle lies in the second quadrant, as shown in the figure below. (Hint: The hexagon can be divided into six congruent triangles.). 3. The Sine Rule can be used in any triangle (not just right-angled triangles) where a side and its opposite angle are known. To find the height of an obtuse triangle, you need to draw a line outside of the triangle down to its base (as opposed to an acute triangle, where the line is inside the triangle or a right angle where the line is a side). Enter three values from a, A, b or B, and we can calculate the others (leave the values blank for the values you do not have): a=, Angle (A)= ° b=, Angle (B)= ° c=, Angle (C)= ° Delbert says that $$\sin \theta = \dfrac{4}{7}$$ in the figure. How to Use the Sine Rule to Find the Unknown Obtuse Angle : High School Math. The angles $$50\degree$$ and $$130\degree$$ are supplementary. \tan \theta \amp = \dfrac{y}{x} = \dfrac{3}{-4} = \dfrac{-3}{4} 2 Answers . Examples 3: Determine sin⁡(α+β) and cos⁡(α+β) if:a. sin⁡α=⅗, cos⁡β=5/13 with α and β are acute angle b. sin⁡α=⅗, cos⁡β=5/13 with α is obtuse angle and β is acute angle x^2 + 1^2 \amp = 3^2\\ \end{align*}, \begin{equation*} Use the inverse cosine key on your calculator to find $$\theta\text{. }$$ Finally, we substitute this expression for $$h$$ into our old formula for the area to get, If a triangle has sides of length $$a$$ and $$b\text{,}$$ and the angle between those two sides is $$\theta\text{,}$$ then the area of the triangle is given by, For the triangle in the lower portion of lot 86, $$a = 120.3\text{,}$$ $$b = 141\text{,}$$ and $$\theta = 95\degree\text{. \(\cos \theta = \dfrac{x}{3}, ~ x \lt 0$$, $$\tan \theta = \dfrac{4}{\alpha}, ~ \alpha \lt 0$$, $$\theta$$ is obtuse and $$\sin \theta = \dfrac{y}{2}$$, $$\theta$$ is obtuse and $$\tan \theta = \dfrac{q}{-7}$$, $$\theta$$ is obtuse and $$\tan \theta = m$$, $$\newcommand{\alert}{\boldsymbol{\color{magenta}{#1}}} Find the sine and cosine of \(130\degree\text{. But the sine of an angle is equal to the sine of its supplement. Watch more videos: DiffGeom15: Quadratic curvature for algebraic curves (cont) 2.9 Related Rates Example 02 (Filling a Trough) One Light Year Equals How Many Miles in Scientific Notation? Use the coordinate definition of the trig ratios #3-20, 45-48, Find the trig ratios of supplementary angles #7-10, 21-38, Know the trig ratios of the special angles in the second quadrant #21, 41-44, Find two solutions of the equation \(\sin \theta = k$$ #29-38. Use the inverse function if needed to find the angle. The line $$y = \dfrac{3}{4}x$$ makes an angle with the positive $$x$$-axis. What about the tangents of supplementary angles? For Problems 35–38, fill in the blanks with complements or supplements. Therefore, ∠B = 90˚ Example 2. To extend our definition of the trigonometric ratios to obtuse angles, we use a Cartesian coordinate system. }\) Give both exact answers and decimal approximations rounded to four places. To find the obtuse angle, simply subtract the acute angle from 180: 180\degree-26.33954244\degree =153.6604576 =154\degree (3 sf). c=36.20. Find the sine inverse of 1 using a scientific calculator. Obtuse Triangle Formulas . The same is true for the supplements of these angles in the second quadrant, shown at right. The Law of Sines (Sine Rule) ... Find the measure of an angle using the inverse sine function: sin-1; Solve a proportion involving trig functions. About this resource. Calculating Missing Side using the Sine Rule. Since we are asked to calculate the size of an angle, then we will use sine rule in the form; Sine (A)/a = Sine (B)/b. }\) Bob presses some buttons on his calculator and reports that $$\theta = 17.46\degree\text{. \endgroup – colormegone Jul 30 '15 at 4:11 \begingroup Yes, once one has the value of \sin \theta in hand, (if it is not equal to 1) one needs to decide whether the angle is more or less than \frac{\pi}{2}, which one can do using, e.g., the dot product. Show all files. The question that I am pondering is that I need to derive the law of cosines for a case in which angle A is an obtuse angle. Now we have completely solved the triangle i.e. Again, a < b. b sin A = 2/2 = , which is less than a. Obtuse Triangles. What is that angle? 5) Identify which Rule is used to find angle FHG (Sine Rule because there is a pair of angle and opposite sides). Yaneli finds that the angle \(\theta$$ opposite the longest side of a triangle satisfies $$\sin \theta = 0.8\text{. A = \dfrac{1}{2} ab \sin \theta In the first of these -- h or b sin A < a -- there will be two triangles. Then CD is the height h of the triangle. \end{equation*}, \begin{equation*} \text{2nd COS}~~~ -3/5~ ) ~~~\text{ENTER } docx, 96 KB. A = \dfrac{1}{2}bh\text{,} \amp = \dfrac{1}{2} (161)((114.8)~\sin 86.1\degree \approx 9220.00 the calculator returns an angle of \(\theta \approx -53.1 \degree\text{. Categories & Ages. }$$ Find the area of the triangle. Finding Angles Using Sine Rule In order to find a missing angle, you need to flip the formula over (second formula of the ones above). \text{First Area}\amp = \dfrac{1}{2}ab\sin \theta\\ }\) To see the second angle, we draw a congruent triangle in the second quadrant as shown. Calculating Missing Angles using the Sine Rule. (. Well, the sine of angle B is going to be its opposite side, AC, over the hypotenuse, AB. }\) Explain Bob's error and give a correct approximation of $$\theta$$ accurate to two decimal places. Compute $$180\degree-\phi\text{. A complete lesson on the scenario of using the sine rule to find an obtuse angle in a triangle. Therefore, b sin A = 2/2 = , which is equal to a. SOLVE THE FOLLOWING USING THE SINE RULE: Problem 1 (Given two angles and a side) In triangle ABC , A = 59°, B = 39° and a = 6.73cm. \cos 135\degree \amp = \dfrac{x}{r} = \dfrac{-1}{\sqrt{2}}\\ }$$ We use the distance formula to find $$r\text{.}$$. }\) Compare to the sine and cosine of $$50\degree\text{. We choose a point \(P$$ on the terminal side of the angle, and form a right triangle by drawing a vertical line from $$P$$ to the $$x$$-axis. Find the coordinates of point P\text{. Lot 86 has an area of approximately 17,669 square feet. \end{equation*}, \begin{align*} Later we will be able to show that \(\sin 18\degree = \dfrac{\sqrt{5} - 1}{4}\text{. \end{align*}, \begin{align*} \sin \theta \amp = \dfrac{y}{r} = \dfrac{3}{5}\\ Find the distance from the origin to point \(P\text{. This is a topic in traditional trigonometry. Find the angle \(\theta \text{,} rounded to tenths of a degree. Code to add this calci to your website Just copy and paste the below code to your webpage where you want to display this calculator. Round to four decimal places. In Chapter 2 we learned that the angles $$30\degree, 45\degree$$ and $$60\degree$$ are useful because we can find exact values for their trigonometric ratios. }\) What is the exact value of $$\sin 162\degree?$$ (Hint: Sketch both angles in standard position. What is that angle? Download Share Share. There is therefore one solution: angle … In this case, we are working with a and c and so we write down the c and the a part of … Write an expression for the area of the triangle. This thereby eliminates the obtuse angle you want. It's rather embarrassing that I'm struggling so much wish this simple trigonometric stuff. Calculate the measure of each side. so $$~\cos 90\degree = 0~$$ and $$~\sin 90\degree = 1~.$$ Also, $$~\tan 90\degree = \dfrac{y}{x} = \dfrac{1}{0}~,$$ so $$\tan 90\degree$$ is undefined. This is also called the arcsine. Since < 2, this is the case a < b.  sin 45° = /2. Find the angle and its supplement, rounded to the nearest degree. Calculate $$\sin \phi,~ \cos \phi\text{,}$$ and $$\tan \phi$$ using the extended definitions listed above. View US version. Find exact values for the base and height of the triangle. (They would be exactlythe same if we used perfect accuracy). First decide which acute angle you would like to solve for, as this will determine which side is opposite your angle of interest. Actions. 4) Question (c), label (a,b,c, ࠵? Solve the equation for the missing side. Here, a > b. In what ratioa)  are the sides? }\) Thus, $$~r=\sqrt{(-1)^2 +1^2} = \sqrt{2}~\text{,}$$ and we calculate, Find exact values for the trigonometric ratios of $$120\degree$$ and $$150\degree\text{.}$$. Therefore there are no solutions. If you want to calculate the size of an angle, you need to use the version of the sine rule where the angles are the numerators. 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