Which expression is equivalent to 5y^-3
1 answer:
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Answer:
Step-by-step explanation:
The altitude falls in the middle of the line.
So, the point at which it falls in the bottom line is the midpoint, so the length of the blue triangle would be 6/2 = 3
So, the blue triangle has length of 3 and height of H and hypotenuse of 10.
Now, we will use Pythagorean Theorem to solve for H. The theorem is:
Leg^2 + Another Leg^2 = Hypotenuse^2
We know one leg of the triangle is 3 and another leg is H and hypotenuse is 10, so we substitute and solve:
This is the exact answer for H
Answer:
(d) 71°
Step-by-step explanation:
The desired angle in the given isosceles triangle can be found a couple of ways. The Law of Cosines can be used, or the definition of the sine of an angle can be used.
<h3>Sine</h3>Since the triangle is isosceles, the bisector of angle W is an altitude of the triangle. The hypotenuse and opposite side with respect to the divided angle are given, so we can use the sine relation.
sin(W/2) = Opposite/Hypotenuse
sin(W/2) = (35/2)/(30) = 7/12
Using the inverse sine function, we find ...
W/2 = arcsin(7/12) ≈ 35.685°
W = 2×36.684° = 71.37°
W ≈ 71°
<h3>Law of cosines</h3>The law of cosines tells you ...
w² = u² +v² -2uv·cos(W)
Solving for W gives ...
W = arccos((u² +v² -w²)/(2uv))
W = arccos((30² +30² -35²)/(2·30·30)) = arccos(575/1800) ≈ 71.37°
W ≈ 71°
