Question

GEOMETRY - NEED HELP - WILL MARK BRAINLIEST

Answer 1

Answer:

Step-by-step explanation:

QUESTION 1

Bottom leg of right triangle= 120 ft

Height= 150 ft

Angle of depression at the top of the tower = x

tan x= adjacent/opposite leg= 150/120= 1.25

tan x= 1.25

x ≈ 51.35°= 51°

QUESTION 2

Cos Z= adjacent side/hypotenuse

Cos Z= 24/30= 4/5

Z= 41.4°

QUESTION 3

Opposite of sine

The cosecant is the reciprocal of the sine

Cosecant Function:

 csc(θ) =  Hypotenuse/Opposite

Answer 2

Answer:

1) 51

2) 0.8

3) cosecant

Step-by-step explanation:

Question 1

The image for this scenario is attached below. Note that base of the television tower forms the side adjacent to the angle and the length of the tower forms the side opposite to the angle. The two angles marked in image are equal because of the property of Alternate Interior Angles.

So,

Adjacent side = 120 feet

Opposite side = 150 feet

Tangent of an angle is defined as:

$tan(\theta)=\frac{Opposite}{Adjacent}$

Using the values, we get:

$tan(\theta)=\frac{150}{120}\\\\ tan(\theta)=1.25\\\\ \theta = tan^{-1}(1.25)\\\\ \theta=51.34$

Rounded to the nearest degree, the angle of depression would be 51 degrees.

Question 2)

We have to find the cosine of angle Z. cos is defined as:

$cos(\theta) = \frac{adjacent}{hypotenuse}$

The side adjacent to angle Z is 24 and the hypotenuse is 30. So cos(Z) would be:

$cos(Z)=\frac{24}{30}\\\\cos(Z)=0.8$

Therefore, value of cos(Z) for given triangle would be 0.8

Question 3

The opposite of sine ratio is known as cosecant which is abbreviated as csc

Since it is the opposite of sine ratio, it would be calculated as:

$csc(\theta)=\frac{1}{sin(\theta)}$

sine of angle is the ratio of opposite and hypotenuse, so csc would be ratio of hypotenuse to opposite side i.e.

$csc(\theta)=\frac{hypotenuse}{opposite}$