sat suite question viewer
Geometry and Trigonometry
Difficulty: Hard
Triangle 
above is a right triangle, and 
. What is the length of side 
?
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Explanation
The correct answer is 24. The sine of an acute angle in a right triangle is equal to the ratio of the length of the side opposite the angle to the length of the hypotenuse. In the triangle shown, the sine of angle B, or 
, is equal to the ratio of the length of side 
to the length of side 
. It’s given that the length of side is 26 and that . Therefore, 
. Multiplying both sides of this equation by 26 yields 
.
By the Pythagorean Theorem, the relationship between the lengths of the sides of triangle ABC is as follows: 
, or 
. Subtracting 100 from both sides of yields 
. Taking the square root of both sides of yields 
.