Question

A ladder leans against the side of a house. The angle of elevation of the ladder is 74° when the bottom of the ladder is 14 feet from the side of the house. Find the length of the ladder. Round your answer to the nearest tenth.

Answer 1

Answer:

50.8 feet

Step-by-step explanation:

We are given that a ladder leans against the side of a house making an angle of elevation of 74° while the distance between the bottom of the ladder and house is 14 feet.

This makes a right angled triangle where have the measure of an angle and the length of the base while hypotenuse is to be found.

So we can use the formula of cos supposing the length of ladder to be x:

$cos 74=\frac{14}{x}$

$x=\frac{14}{cos 74} =50.8$

Therefore, the length of the ladder is 50.8 feet.

Answer 2

Answer:

The length of the ladder is 50.8 ft

Step-by-step explanation:

we are given

the angle of elevation of the ladder is 74° when the bottom of the ladder is 14 feet from the side of the house

So, firstly, we will draw diagram

we can see that

angle =74

base length =14

we have to find hypotenuse

so, we can use trig formula

$cos(74)=\frac{14}{L}$

now, we can solve for L

$L=\frac{14}{cos(74)}$

we get

$L=50.7913ft$

So,

The length of the ladder is 50.8 ft