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?

An Example to get to your answer to your awesome question! Hope you can learn from it and find your answer!

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.

step-by-step explanation:

let

we know that

the y-intercept is the y-coordinate of the point when the value of x is equal to zero

so

the y-coordinate of the point a is the y-intercept

the answer part a) is

the value of y-intercept is

part b) find the slope m

we know that

the value of the slope is equal to

substitute the values

therefore

the answer part b) is

the value of the slope is equal to

the general answer is

the slope is

the value of y-intercept is