Question

In triangle ABC, with right angle at C, if c=6 and a=4, the CosA=

Answer 1

cos A = √20/6 ≈ 0.75

Step-by-step explanation

Triangle ABC is:

Since this is a right triangle we can use the trigonometric ratios to find cosA:

`\cos A=\frac{\text{adjacent side}}{hypotenuse}`

the hypotenuse of this triangle is side c, and the adjacent side is side b. We don't have side b, but we have two sides and again, as this is a right triangle, we can use the Pythagorean theorem to find the missing side:

`\begin{gathered} c^2=a^2+b^2 \\ b=\sqrt[]{c^2-a^2} \\ b=\sqrt[]{6^2-4^2} \\ b=\sqrt[]{36-16} \\ b=\sqrt[]{20} \end{gathered}`

The cosine of A is then:

`\cos A=(b)/(c)=\frac{\sqrt[]{20}}{6}`

Rounded to the nearest hundredth:

`\cos A\approx0.75`