Question

Example 6.25 Two trees are standing on flat ground. The angle of elevation of the top of
both the trees from a point X on the ground is 40°. If the horizontal distance between X
and the smaller tree is 8 m and the distance of the top of the two trees is 20 m, calculate
(i) the distance between the point X and the top of the smaller tree.
(ii) the horizontal distance between the two trees.
(cos 40º = 0.7660)​

Answer 1

Answer:

1)

Step-by-step explanation:

cos=adj/hyp

cos40°=CX/XD

XD=8/0.7660

=10.44m

hence the distance between the top of the tree to the small tree is 10.44

Answer 2

The distance between the X and the top of  the smaller tree is the 10.44 m

The horizontal distance between the two trees is 15.32 m  

Step-by-step explanation:

let AB be the height of the  bigger tree

CD be the height of the smaller tree

and X is the point on the ground

(i)  in right triangle CXD

$\cos 40^\circ = \frac{CX}{XD}\\\\XD = \frac{8}{0.7660}= 10.44 m$

therefore , The distance between the X and the top of  the smaller tree is the XD = 10.44 m

now,

(ii) in right triangle AXB

$\cos 40^\circ = \frac{AX}{BX}\\\\\cos 40^\circ= \frac{AC+CX}{BD +DX}\\\\0.7660 = \frac{AC +8}{20+10.44}\\\\AC =23.32-8 \\\\AC = 15.32$

therefore ,

The horizontal distance between the two trees is AC = 15.32

#Learn more :

https://brainly.in/question/11390285