Question

The length of the hypotenuse line segment AC in right triangle ABC is 25 cm. The length of line segment BC is 15 centimeters. What is the approximate measure of angle ACB?

Answer 1

From my understanding you ahould use the trig function cos to solve this.
cos(c) = 15/25 or 0.6
if you have this following function on your calculator I suggest using it:

cos ^{ - 1}

by using the function like so:

cos^{ - 1} (0.6

you should get about 53.13° (rounding to the nearest hundredth)
Hope this helped.

Answer 2

The approximate measure of angle ACB is 53.13°

Explanation:

Given,

In the right triangle ABC,

AC = 25 cm,

BC = 15 cm,

Where, AC is the hypotenuse of the triangle,

⇒ ∠B = 90°

By the pythagoras theorem,

`AB^2=AC^2-BC^2=25^2-15^2=625 - 225 = 400`

`\implies AB=20\text{ cm}`

Now, by the law of sine,

`(sin C)/(AB)=(sin B)/(AC)`

`\implies sin C=(AB* sin B)/(AC)`

By substituting the values,

`sin C=(20* sin 90^(\circ))/(25)=(20)/(25)=0.8`

`\angle C=53.1301023542\approx 53.13^(\circ)`

Hence, the approximate measure of angle ACB is 53.13°