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Sagot :
Answer:The tree is 186.6 feet tall.
Step-by-step explanation:SOH-CAH-
T
OA
\text{tan }\color{purple}{64}=\frac{\color{green}{\text{opposite}}}{\color{blue}{\text{adjacent}}}=\frac{\color{green}{x}}{\color{blue}{91}}
tan 64=
adjacent
opposite
=
91
x
\text{tan }64=
tan 64=
\,\,\frac{x}{91}
91
x
\frac{\text{tan }64}{1}=
1
tan 64
=
\,\,\frac{x}{91}
91
x
91\text{ tan }64=
91 tan 64=
\,\,x
x
Cross multiply.
x=186.577649...\approx186.6
x=186.577649...≈186.6
Type into calculator and round to the nearest tenth.
\text{The tree is 186.6 feet tall.}
The tree is 186.6 feet tall.
The height of the considered tree if the point on the ground is 91 feet from the tree is 186.6 feet approximately.
What is angle of elevation?
You look straight parallel to ground. But when you have to watch something high, then you take your sight up by moving your head up. The angle from horizontal to the point where you stopped your head is called angle of elevation.
For this case, referring to the attached figure below, we get:
- Angle of elevation = [tex]m\angle ACB = 64^\circ[/tex]
- Distance of the base of the tree from the point of the ground = 91 feet
- Height of the considered tree = h feet (assume).
Angle ACB denotes internal angle made by AC and CB line segments). It is the angle of elevation here, taking BC as horizontal line, and AC as elevated line.
Then, using the tangent ratio from the perspective of angle ACB, we get:
[tex]\tan(m\angle ACB) = \dfrac{|AB|}{|BC|} \\\tan(64^\circ)= \dfrac{h}{91}\\\\h = 91 \times \tan(64^\circ)[/tex]
From calculator, we get: [tex]\tan(64^\circ) \approx 2.05[/tex], thus:
[tex]h \approx 91 \times 2.05 = 186.55 \approx 186.6 \: \rm ft[/tex]
Thus, the height of the considered tree if the point on the ground is 91 feet from the tree is 186.6 feet approximately.
Learn more about tangent ratio here:
https://brainly.com/question/14169279
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