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
[tex]\cos A=\dfrac{15}{17}\\\\\tan A=\dfrac{8}{15}[/tex]
To Find:
BC = ?
Solution:
In Right Angle Triangle ABC, Cosine and Tangent identity
[tex]\cos A = \dfrac{\textrm{side adjacent to angle C}}{Hypotenuse}\\[/tex]
[tex]\tan A= \dfrac{\textrm{side opposite to angle A}}{\textrm{side adjacent to angle A}}[/tex]
BUT,
[tex]\cos A=\dfrac{15}{17}\\\\\tan A=\dfrac{8}{15}[/tex] ....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,
[tex](\textrm{Hypotenuse})^{2} = (\textrm{Shorter leg})^{2}+(\textrm{Longer leg})^{2}[/tex]
[tex](\textrm{Hypotenuse})^{2} = 17^{2}=289[/tex]
[tex](\textrm{Shorter leg})^{2}+(\textrm{Longer leg})^{2}=15^{2}+8^{2}=289[/tex]
The Figure for Right triangle is below,
Therefore , 15 unit length represents BC.
