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

The expression is read the inverse sine of x and is interpreted as the angle with sine x.Use the thought:If the 30°≈.058, then

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] 13 1946.82644889

2nd ( ÷ ) 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 1 Find mA by using a tangent ratio.

29.7448813 ≈ mA Use a calculator.

So, the measure of A is about 30.

Definition of inverse

tangent

Step 2 Find mB using complementary angles.

mB ≈ 60 Subtract 30 fromeach side.

So, the measure of B is about 60.

30 + mB ≈ 90 mA ≈ 30

mA + mB =90 Definition ofcomplementaryangles

Step 3 Find AB by using the Pythagorean Theorem.

(AC)2 + (BC)2 = (AB)2 Pythagorean Theorem

72 + 42 = (AB)2 Substitution

65 = (AB)2 Simplify.

Take the positivesquare root of eachside.

8.06 ≈ AB Use a calculator.

Answer: mA ≈ 30, mB ≈ 60, AB ≈ 8.06

So, the measure of AB is about 8.06.

A. mA = 36°, mB = 54°, AB = 13.6

B. mA = 54°, mB = 36°, AB = 13.6

C. mA = 36°, mB = 54°, AB = 16.3

D. mA = 54°, mB = 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