Question

a tower leans at an angle of about 84.7°. the figure shows that 172 feet from the base of the tower the angle of elevation to the top is 49.8°. find the distance to the nearest foot from the base to the top of the tower

Answer 1

the distance to the nearest foot from the base to the top of the tower is 184 feet .

Step-by-step explanation:

Here we have , a tower leans at an angle of about 84.7°. the figure shows that 172 feet from the base of the tower the angle of elevation to the top is 49.8°. We need to find the distance to the nearest foot from the base to the top of the tower . Let's find out:

Let angle A = 49.8

Let Angle B = 84.7

Since the angles of a triangle must add up to 180, then

Angle C = 180-49.8-84.7 = 45.5

Now, use the law of sines to find the distance from the base to the top of the tower. That is the side of the triangle opposite Angle A. The distance of 172 feet is the side opposite Angle C. So:

⇒ $\frac{a}{sin(a)}= \frac{c}{sin(c)}$

⇒ $\frac{a}{sin(49.8)}= \frac{172}{sin(45.5)}$

⇒ $a= \frac{172}{sin(45.5)}(sin(49.8)$

⇒ $a= \frac{172}{0.71}(0.76)$

⇒ $a=184ft$

Therefore , the distance to the nearest foot from the base to the top of the tower is 184 feet .

Answer 2

The distance from the base to the top of the tower is $161 feet$ to the nearest foot.

What we are trying to find is how "long" the tower is.

The sine rule will be used to derive the distance from the base to the top of the tower.

First get the angle B by subtracting the angles given from 180 degrees.

So, given the sine rule formula

$\frac{d}{sin D}=\frac{b}{sin B}$

We can make d the subject, substitute and solve

$d=b\times \frac{sin B}{sin D}=172\times \frac{sin 134.5}{sin 49.8}=161 feet$

Learn more about the sine rule: https://brainly.com/question/20360487