Aladder leans against the side of a house. the angle of elevation of the ladder is 64 degrees , and the top of the ladder is 13 ft from the ground. find the length of the ladder. round your answer to the nearest tenth.

The length of the ladder is 14.5 ft

Step-by-step explanation:

For a right triangle

sinx = opposite / hypotenuse

Since we know the angle and the opposite side, we can calculate the hypotenuse

sin 64 = 13/ hypotenuse

Multiply each side by the hypotenuse

hypotenuse * sin 64 = 13

Divide by sin 64

hypotenuse = 13/sin 64

hypotenuse=14.4638

Rounding to the nearest tenth

14.5

(sin 42)/31. = sinx)/37

sinx = 37 (sin42)/31

= 37× 0.66/31 = 0.787

x= 51.9

other angle opposite to y = 180-51.9-42

= 180- 93.9 =86.1

so

sin42)/31 = sin 86.1)/y

0.021 = 0.997 /y

y= 0.997/0.021 =47.47