Answer:
Height of tree is [tex]\approx[/tex] 15 m.
Step-by-step explanation:
Given that student is 20 m away from the foot of tree.
and table is 1.5 m above the ground.
The angle of elevation is: 34°28'
Please refer to the attached image. The given situation can be mapped to a right angled triangle as shown in the image.
AB = CP = 20 m
CA = PB = 1.5 m
[tex]\angle C[/tex] = 34°28' = 34.46°
To find TB = ?
we can use trigonometric function tangent to find TP in right angled [tex]\triangle TPC[/tex]
[tex]tan \theta = \dfrac{Perpendicular}{Base}\\tan C= \dfrac{PT}{PC}\\\Rightarrow tan 34.46^\circ = \dfrac{PT}{20}\\\Rightarrow PT = 20 \times 0.686 \\\Rightarrow PT = 13.72\ m[/tex]
Now, adding PB to TP will give us the height of tree, TB
Now, height of tree TB = TP + PB
TB = 13.72 + 1.5 = 15.22 [tex]\approx[/tex] 15 m
