BackSolve each problem. (Source for Exercises 49 and 50: Parker, M., Editor, She Does Math, Mathematical Association of America.) Length of Sides of an Isosceles Triangle An isosceles triangle has a base of length 49.28 m. The angle opposite the base is 58.746°. Find the length of each of the two equal sides.
Determine whether each statement is possible or impossible. See Example 4. tan θ = 0.93
Solve each problem. (Source for Exercises 49 and 50: Parker, M., Editor, She Does Math, Mathematical Association of America.) Find a formula for h in terms of k, A, and B. Assume A < B.
Solve each problem. (Source for Exercises 49 and 50: Parker, M., Editor, She Does Math, Mathematical Association of America.) Create a right triangle problem whose solution can be found by evaluating θ if sin θ = ¾.
In Exercises 61–62, use the figures shown to find the bearing from O to A.
Determine whether each statement is possible or impossible. See Example 4. cot θ = ―6
Use identities to solve each of the following. Rationalize denominators when applicable. See Examples 5–7. Find csc θ , given that cot θ = ―1/2 and θ is in quadrant IV.
Use identities to solve each of the following. Rationalize denominators when applicable. See Examples 5–7. Find cot θ , given that csc θ = ―1.45 and θ is in quadrant III.
If θ is an acute angle and cos θ = 1/3, find csc (𝜋/2 - θ).
Give all six trigonometric function values for each angle θ. Rationalize denominators when applicable. See Examples 5–7. tan θ = ―15/8 , and θ is in quadrant II .
Give all six trigonometric function values for each angle θ. Rationalize denominators when applicable. See Examples 5–7.
sin θ = √5/7 , and θ is in quadrant I.
Give all six trigonometric function values for each angle θ. Rationalize denominators when applicable. See Examples 5–7.
sin θ = √2/6 , and cos θ < 0
Give all six trigonometric function values for each angle θ. Rationalize denominators when applicable. See Examples 5–7.
cos θ = 1
Concept Check Suppose that 90° < θ < 180° . Find the sign of each function value. tan θ/2
Concept Check Suppose that 90° < θ < 180° . Find the sign of each function value. cot (θ + 180°)