Question

In ΔABC, the measure of ∠C=90°, the measure of ∠A=49°, and BC = 5.1 feet. Find the length of AB to the nearest tenth of a foot.

Answer 1

To find the length of AB to the nearest tenth of a foot in a right-angled triangle where one angle is 49° and one side is 5.1 feet, use the trigonometric cosine function, yielding a result of approximately 7.8 feet.

Step-by-step explanation:

To find the length of AB in the right-angled triangle ΔABC, where the measure of ∠C is 90°, the measure of ∠A is 49°, and side BC is 5.1 feet, we can use the trigonometric functions. Considering that AB is the hypotenuse and BC is the adjacent side to ∠A, we can use the cosine function. The cosine of ∠A (cos 49°) is equal to the adjacent side (BC) over the hypotenuse (AB), which can be represented as cos(49°) = BC/AB.

We are given BC = 5.1 feet, so we can solve for AB:

cos(49°) = 5.1 feet / AB
AB = 5.1 feet / cos(49°)

By calculating this, we would get:

AB ≈ 7.8 feet

Therefore, the length of AB is approximately 7.8 feet to the nearest tenth of a foot.