Answer to Question #197466 in Geometry for Andu

Question

The figure shows two right-angled triangles. The first triangle has one floor 6 cm and another 10cm, and has a narrow angle = x. The second triangle has sides with length: y cm and 15 cm as well as a narrow angle = x. The value of y is:

A. 11

B. 9

C. 7.5

D. 4

Answer 1

Given two triangles with respective side length in the figure below:

So, Applying trigonometry in both the triangles

$\text{In triangle-1}\\tanx=\dfrac{10}{6}=\dfrac{5}{3}$ ......(i)

and In traingle-2

$tanx =\dfrac{15}{y}\ ......(ii)$

from equations (i) and (ii)

$\Rightarrow \dfrac{15}{y}=\dfrac{5}{3}\\\ \\\Rightarrow y=\dfrac{15\times 3}{5}=9\\\ \\Hence, y=9$

Answer:

$\boxed{[B] \ \ y=9}$