In ΔUVW, the measure of ∠W=90°, UW = 35, VU = 37, and WV = 12. What is the value of the tangent of ∠U to the nearest hundredth?

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Step-by-step explanation:

Example 1 Find Sine, Cosine, and Tangent Ratios

Find sin A, cos A, tan A, sin B, cos B, and tan B.

Express each ratio as a fraction and as a decimal.

Round to the nearest hundredth.

sin A =

opposite leg

hypotenuse

=

BC

AB

=

12

13 or 0.92

cos A =

adjacent leg

hypotenuse

=

AC

AB

=

5

13 or 0.38

tan A =

opposite leg

adjacent leg

=

BC

AC

=

12

5

or 2.4

sin B =

opposite leg

hypotenuse

=

AC

AB

=

5

13 or 0.38

cos B =

adjacent leg

hypotenuse

=

BC

AB

=

12

13 or 0.92

tan B =

opposite leg

adjacent leg

=

AC

AB

=

5

12 or 0.42

Example 2 Evaluate Expressions

Use a calculator to find each value to the nearest ten thousandth.

a. cos 48°

KEYSTROKES: [COS] 48 [ENTER]

cos 48° ≈ 0.6691

b. sin 85°

KEYSTROKES: [SIN] 85 [ENTER]

sin 85° ≈ 0.9962

Example 3 Use Trigonometric Ratios to Find a Length

AVIATION A plane in flight begins to climb at a constant angle of 2° for the next 70 ground miles.

Find the change in the plane's altitude to the nearest tenth mile.

Let x be the change in altitude in miles.

tan 2° =

x

70 tan =

leg opposite

leg adjacent

70 tan 2° = x Multiply each side by 70.

Use a calculator to find x.

KEYSTROKES: 70 [TAN] 2 [ENTER] 2.444453864

The change in the plane's altitude is about 2.4 miles.

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