Answer:
[tex]tan(A) = \frac{3}{4}[/tex]
Step-by-step explanation:
Given
Right-angled triangle ABC
[tex]c = 10[/tex] [tex]b = 8[/tex]
Required
Calculated tan(A)
First, we calculate the length of a.
Since the triangle is right-angled at C, then c is the hypotenuse and side a is the opposite of A.
So, we have:
[tex]c^2 = a^2 + b^2[/tex]
[tex]10^2 = a^2 + 8^2[/tex]
[tex]100 = a^2 + 64[/tex]
[tex]a^2 = 100 - 64[/tex]
[tex]a^2 = 36[/tex]
Take square roots
[tex]a = 6[/tex]
So:
[tex]tan(A) = \frac{a}{b}[/tex]
[tex]tan(A) = \frac{6}{8}[/tex]
[tex]tan(A) = \frac{3}{4}[/tex]
