So if you want to round to the nearest tenth, then you can write the result 29.5°.
Introduction
Hi ! I'm Deva from Brainly Indonesia, I will help you solve problems using the Pythagorean Theorem. The Pythagorean theorem is usually used to express the relationship between the base, height, and hypotenuse sides of the various possible planes to form a right triangle pattern. The basic equation of the Pythagorean Theorem, namely :
[tex] \boxed{\sf{\bold{c^2 = a^2 + b^2}}} [/tex]
[tex] \boxed{\sf{\bold{b^2 = c^2 - a^2}}} [/tex]
[tex] \boxed{\sf{\bold{a^2 = c^2 - b^2}}} [/tex]
With the following conditions :
- a = base side of right triangle
- b = perpendicular side (height) of a right triangle
- c = right triangle hypotenuse
Problem Solving
We know that :
- a = [tex] \sf{\overline{UV}} [/tex] = 67
- c = [tex] \sf{\overline{TV}} [/tex] = 77
What to ask :
- x = measure of angle x = ... °
Step by step :
- Find the value of b [tex] \sf{\overline{TU}} [/tex]
[tex] \sf{b^2 = c^2 - a^2} [/tex]
[tex] \sf{b = \sqrt{c^2 - a^2}} [/tex]
[tex] \sf{b = \sqrt{77^2 - 67^2}} [/tex]
[tex] \sf{b = \sqrt{5,929 - 4,489}} [/tex]
[tex] \sf{b = \sqrt{1440}} [/tex]
[tex] \sf{b \approx 37.95} [/tex]
- Find the value of the angle x°. See that [tex] \sf{\overline{TU}} [/tex] is in front of the angle x°. We can use the sine which is the ratio of the opposite side of the angle to the length of the hypotenuse.
[tex] \sf{\sin x = \frac{\overline{TU}}{\overline{TV}}} [/tex]
[tex] \sf{\sin x = \frac{37.95}{77}} [/tex]
[tex] \sf{\sin x \approx 0.493} [/tex]
[tex] \sf{x \approx \sin^{-1} 0.493} [/tex]
[tex] \sf{x \approx 29.54^o} [/tex]
So if you want to round to the nearest tenth, then you can write the result 29.5°
