Question

#1 Given: ABC is a right triangle with right angle C. AB=18 centimeters and m∠A=22∘ . What is BC ?

#2 A wooden board is leaning against a house. The base of the board is 10 feet from the base of the house, and the base of the board forms a 35° angle with the ground.

What is the length of the wooden board?

Answer 1

1. The length of BC is 7.923
2. the length of the wooden board is 11.066

Answer 2

Answer: BC= 0.59 cm ( approx) and length of wooden board = 12.21 ( approx)

Explanation:

In first question,

In triangle ABC,

Since C is the right angle.

Therefore Sin A =
`(BC)/(18)`

⇒ Sin 22°=
`(BC)/(18)`

⇒BC= 18× Sin22°=0.5877852552≈0.59 centimeter.

Now in second question,

Let L represent the length of board and x represents the distance of board from the foot of house.

Therefore Cos 35° =10/L ⇒ L =10/ Cos 35°= 12.2077456≈12.21 cm