Question

In A ABC. AB = 6 cm, AC = 15 cm, and mA = 48° What is the area of A ABC? Enter your answer as a decimal in the box. Round only your final answer to the nearest hundredth.​

Answer 1

To find the area of triangle ABC, we can use the formula A = (1/2) * b * h, where b is the base of the triangle and h is its height. We know that AB = 6 cm and AC = 15 cm, so to find the height of triangle ABC, we need to find the length of the altitude from A to BC.

To find the length of the altitude, we can use trigonometry. Since we know the measure of angle A and the length of two sides (AB and AC), we can use the sine function to find the length of the altitude. Specifically, we can use the formula h = AC * sin(A).

Plugging in the values we have, we get:

h = 15 cm * sin(48°) h ≈ 11.32 cm

Now that we have the height, we can find the area of triangle ABC:

A = (1/2) * AB * h A = (1/2) * 6 cm * 11.32 cm A ≈ 33.96 cm²

So the area of triangle ABC is approximately 33.96 cm². Rounded to the nearest hundredth, the answer is 33.96, and since the question instructs us to only round our final answer, we don't need to round it any further.

Explanation: