What values of x make the two expressions below equal?
2 answers:
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Answer:
m∠Q ≈ 53°
Step-by-step explanation:
To find the measure of ∠Q, the law of cosines will need to be used. Lowercase letters represent the side lengths, while upper case letters represent angles.
In this situation, 'A' will be ∠Q. Therefore:
17² = 18² + 20² -2(18)(20)cosQ
Simplify:
289 = 324 + 400 -2(360)cosQ
Continue simplifying down:
-435 = -720cosQ
Divide both sides by '-720':
0.604 = cosQ
m∠Q ≈ 52.83 or 53° rounded to the nearest whole degree.
From the given picture, we can see that 2 sides are congruen, then the given triangle is an isosceles triangle. In this triangle the base angles are congruent, so we can draw the following picture:
Now, since interior angles of any triangle add up to 180 degrees, we have
By combining similar terms, we get
Then, x is given as
Therefore, the answer is x=90 degrees
