Question

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In right ABC angle c is the right angle, AC = 7, and BC = 24. Find the value of the sine of the largest acute angle of the triangle.

Answer 1

Answer:

Step-by-step explanation:

Remark

AC and BC are the legs of a triangle. You are told that the right angle is at C. Both these sides have one endpoint  C. That means that they are the shorter of the three lines. The first thing we must do is find the Hypotenuse. You need the Hypotenuse to get the sin of one or both of the acute angles.

Hypotenuse

a^2 + b^2 = c^2

a = 7

b = 24

c = ?

c^2 = 7^2 + 24^2  

c^2 = 49 + 576

c^2 = 625

sqrt(c^2) = sqrt(625)

c = 25

Find the Largest Angle

The largest angle is going to be opposite the longest leg (not the Hypotenuse although you use the hypotenuse).

Sin(A) = 24/ 25

Sin(A) = 0.96

A = Sin-1(0.96)

A = 73.74