2.) matt is standing on top of a cliff 305 feet above a lake. the measurement of the angle of depression to a boat on the lake is 42 degrees . how far is the boat from the base of the cliff?

The boat is 338.7 feet away from the base of the cliff.

EXPLANATION

Let be the distance of the boat from the base of the cliff.

We can use alternate angles property to bring the angle of depression into the triangle.

Since the known side is opposite the angle and the sede we are finding is adjacent to it, we use the tangent ratio.

From the diagram,

Hence the boat is 338.7 feet away from the base of the cliff.

Using the concept of trigonometry, the distance of the boat from the base of the cliff is 338.74 feets

Recall :

Tan θ = opposite / Adjacent = height / base distance

Tan 42° = 305 / d

0.9004040 = 305 / d

d = 305 / 0.9004040

d = 338.74 feets.

Therefore, the distance from the base is 338.74 feets

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9) i can't see the angle so whatever it is just do this: cos(angle) x hypotenuse and then use that answer and they hypotenuse and plug it into this: (answer you just got)^2 + b^2 = (hypotenuse)^2. the first answer will be the answer of the adjacent side and the second answer after this equation will be the opposite side.

10) y = 14 x = √147 or 12.12435565

11) x = 4.8

12) x = 4.2

13) x = 9.3

14) pq: 13.2

qr : 17.6

angle p: 53º

15) angle c: 54.3º

angle a: 35.7º

16) h = 21040

v = 1841

step-by-step explanation:

10) 7/sin(30) = 14 = y

7^2 + b^2 = 14^2

49 + b^2 = 196

b^2 = 196 - 49

√b^2 = √147

x = √147

11) cos(70) x 14 = 4.788282007

x = 4.8

12) tan(25) x 9 = 4.196768923

x = 4.2

13) sin(31) x 18 = 9.270685348

x = 9.3

14) pq: sin(37) x 22 = 13.23993051

pq: 13.2

qr: cos(37) x 22 = 17.56998122

qr : 17.6

angle p: 180 - (37 + 90) = 53º

15) cos-1(7/12) = 54.31466529

angle c: 54.3º

angle a: 180 - (90 + 54.31466529) = 35.68533471

angle a: 35.7º

16) 4 x 5280 = 21120

cos(5) x 21120

h = 21039.63202

h = 21040

sin(5) x 21120

v = 1840.729287

v = 1841