Question

question 11 (1 point)
for the given triangle, cos a is equal to which expression?
20 cm
a
15 cm
a) \\( \frac { 4 } { 5 } \\)
b) \\( \frac { 3 } { 5 } \\)
c) \\( \frac { 3 } { 4 } \\)
d) \\( \frac { 4 } { 3 } \\)

Explanation:

Step1: Find the hypotenuse

Use the Pythagorean theorem \(c=\sqrt{a^{2}+b^{2}}\), where \(a = 15\) and \(b=20\).
\(c=\sqrt{15^{2}+20^{2}}=\sqrt{225 + 400}=\sqrt{625}=25\)

Step2: Calculate \(\cos A\)

By the definition of cosine in a right - triangle \(\cos A=\frac{\text{adjacent}}{\text{hypotenuse}}\).
The adjacent side to angle \(A\) is \(15\) and the hypotenuse is \(25\). So \(\cos A=\frac{15}{25}=\frac{3}{5}\)

Answer:

B. \(\frac{3}{5}\)