Aladder is leaning against a wall and make an 82 degree angle of elevation with the ground. part a: if the base of the ladder is 4 feet from the wall, then how long is the ladder? round to the nearest tenth. part b: determine how high up the wall does the ladder reach.

A) The length of Ladder is 28.7 feet.

B)The length of the wall up to where the ladder reaches is 28.5 feet.

Step-by-step explanation:

Consider a wall AB and a ladder AC .

The ladder is  leaning against a wall and make an 82 degree angle of elevation with the ground that is ∠ACB = 82°

Part A)  If the base of the ladder is 4 feet from the wall that is  BC= 4 feet.

We have to find the length of ladder (AC).

Consider Δ ABC , with ∠B= 90°

Applying trigonometric ratio,

Substitute the values, we get,

Solve for AC, we get,

(approx)

Thus, the length of Ladder is 28.7 feet.

B) To determine the length  of the wall up to where the ladder reaches,

Applying trigonometric ratio,

Substitute the values, we get,

Solve for AB, we get,

(approx)  

Thus, the length of the wall up to where the ladder reaches is 28.5 feet.

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