Solving for Angle Measures of Right Triangles — Quiz

Question 2 • Integrated Math II CR SUSD (EX)

In which triangle is the value of x equal to cosine inverse of open paren 4 point 3 over 6 point 7 close paren ? (Images may not be drawn to scale.)

Answer

Image with description A right triangle is shown. The length of the hypotenuse is 6 point 7 and the length of another side is 4 point 3. The angle opposite to side with length 4 point 3 is x.

Image with description A right triangle is shown. The length of the hypotenuse is 4 point 3 and the length of another side is 6 point 7. The angle between 2 sides is x.

Image with description A right triangle is shown. The length of the hypotenuse is 6 point 7 and the length of another side is 4 point 3. The angle between the 2 sides is x.

Image with description A right triangle is shown. The length of the 2 sides are 6 point 7 and 4 point 3. The angle opposite to side with length 4 point 3 is x.

Explanation

For a right triangle, cos(x) = adjacent side ÷ hypotenuse. The expression 4.3 ÷ 6.7 means the side of length 4.3 must be adjacent to angle x, while 6.7 is the hypotenuse. Choice D shows the angle between those two sides, so x = cos⁻¹(4.3 ÷ 6.7).

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