The two triangles are similar. <span>When two </span>figures<span> are </span>similar<span>, the ratios of the lengths of their corresponding sides are equal. We use this fact in order to calculate the height of the bigger triangle. We do as follows:
QP / SL = MN / SL+SR
25 / SL = 35 / SL + 13
SL = 32.5
Area = height x base / 2
Area = SL x MN / 2
Area = 32.5 x 35 / 2 = 568.75
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Answer:
Step-by-step explanation:
You know that ...
- cos(θ)² = 1 - sin(θ)²
- tan(θ) = sin(θ)/cos(θ)
- cosine is negative in the third quadrant (where π < θ < 3π/2)
Using what you know about the relationships of these trig functions, you can find ...
cos(θ)² = 1 - ((-√3)/2)² = 1 - 3/4 = 1/4
cos(θ) = -1/2 . . . . . negative square root of 1/4
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tan(θ) = sin(θ)/cos(θ) = ((-√3)/2)/(-1/2)
tan(θ) = √3
Step-by-step explanation:
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