Question

Consider the right triangle ABC given below use the 25° angle in the sine ratio to find the length of side B to two decimal places

Answer 1

Part II = 22.66

Explanation:

The other answer did great but I will correct that in Part 2 Pythagorean Theorem Method the user said 20.66 instead of 22.66. The correct answer is 22.66

Answer 2

the complete question in the attached figure

Part a) find the length of side B to two decimal places

we know that
sin 25=opposite side angle 25/hypotenuse
opposite side angle 25=b
hypotenuse=25
so
sin 25=b/25-----> b=25*sin 25-----> b=10.565-----> b=10.57

the answer Part a) is
b=10.57

Part b) Find the length of side a in three different ways
1) using cos 25
cos 25=adjacent side angle 25/hypotenuse
adjacent side angle 25=a
hypotenuse=25
so
cos 25=a/25-----> a=25*cos 25----> a=22.66

2) using tan 25
tan 25=opposite side/adjacent side
tan 25=b/a-----> a=b/tan 25----> a=10.57/tan 25----> a=22.66

3) using Pythagoras theorem
we know that
hypotenuse²=a²+b²----> a²=hypotenuse²-b²----> a²=25²-10.57²
a²=513.275-----> a=20.66