8-4 Trigonometry, day 2 You used the Pythagorean Theorem to find missing lengths in right triangles. Find trigonometric ratios using right triangles. Use trigonometric ratios to find angle measures in right triangles.

You can use a calculator to find the measure of an angle which is the inverse of the trigonometric ratio (sine, cosine, or tangent of an acute angle). p. 571

Inverse Trigonometric Ratios

Use a calculator to find the measure of  P to the nearest tenth. The measures given are those of the leg adjacent to  P and the hypotenuse, so write the equation using the cosine ratio. KEYSTROKES: [COS] nd( ÷)ENTER Answer: So, the measure of  P is approximately 46.8°.

A.44.1° B.48.3° C.55.4° D.57.2° Use a calculator to find the measure of  D to the nearest tenth.

Solve the right triangle. Round side measures to the nearest hundredth and angle measures to the nearest degree. Step 1Find m  A by using a tangent ratio ≈m  AUse a calculator. So, the measure of  A is about 30 . Definition of inverse tangent

Step 2Find m  B using complementary angles. m  B≈60Subtract 30 from each side. So, the measure of  B is about 60  m  B≈90m  A ≈ 30 m  A + m  B =90Definition of complementary angles

Step 3Find AB by using the Pythagorean Theorem. (AC) 2 + (BC) 2 =(AB) 2 Pythagorean Theorem =(AB) 2 Substitution 65=(AB) 2 Simplify. Take the positive square root of each side. 8.06≈ ABUse a calculator. Answer: m  A ≈ 30, m  B ≈ 60, AB ≈ 8.06 So, the measure of AB is about 8.06.

A.m  A = 36°, m  B = 54°, AB = 13.6 B.m  A = 54°, m  B = 36°, AB = 13.6 C.m  A = 36°, m  B = 54°, AB = 16.3 D.m  A = 54°, m  B = 36°, AB = 16.3 Solve the right triangle. Round side measures to the nearest tenth and angle measures to the nearest degree.

8-4 Assignment day 2 Page 573, 12-15, 36-39, 42-44