Question

Given the right triangle shown below.if Cos A =15/17 and tan A=8/15 which of the following represents the length of BC

Answer 1

Answer:

The Figure for Right triangle is below,

Therefore , 15 unit length represents BC.

Step-by-step explanation:

Given:

Consider a right triangle ABC, Such that

$\cos A=\dfrac{15}{17}\\\\\tan A=\dfrac{8}{15}$

To Find:

BC = ?

Solution:

In Right Angle Triangle ABC, Cosine and Tangent identity

$\cos A = \dfrac{\textrm{side adjacent to angle C}}{Hypotenuse}$

$\tan A= \dfrac{\textrm{side opposite to angle A}}{\textrm{side adjacent to angle A}}$

BUT,

$\cos A=\dfrac{15}{17}\\\\\tan A=\dfrac{8}{15}$ ....Given

On Comparing,

Adjacent side to angle A = AB = 15

Opposite side to angle A = BC = 8

Hypotenuse = AC =17

Also Pythagoras theorem is Satisfies,

$(\textrm{Hypotenuse})^{2} = (\textrm{Shorter leg})^{2}+(\textrm{Longer leg})^{2}$

$(\textrm{Hypotenuse})^{2} = 17^{2}=289$

$(\textrm{Shorter leg})^{2}+(\textrm{Longer leg})^{2}=15^{2}+8^{2}=289$

The Figure for Right triangle is below,

Therefore , 15 unit length represents BC.