Question

How do you find the base of a right triangle when given the hypotenuse is 14 ft. the angle formed between the hypotenuse and base is 41 degrees?

Answer 1

`a = 10.57\quad ft`

Explanation:

There's a relationship that exists between the sides of a right triangle. These are called the trigonometric identities. The three basics are:

`sin(\theta)=\frac{o}{h}`

`cos(\theta)=\frac{a}{h}`

`tan(\theta)=\frac{o}{a}=\frac{sin(\theta)}{cos(\theta)}`

There's a useful mnemonic you can use to remember them:

S ine
O pposite
H ypothenuse

C osine
A djacent
H ypothenuse

T angent
O pposite
A djacent

So, given the hypothenuse and the angle formed between it and its base (adjacent side), the relationship formed is the cosine:

`cos(\theta)=\frac{a}{h}`

Since we know the angle `\theta=41^\circ` and the hypothenuse `h=14ft`, all we need to do is to solve for its adjacent side `a`.

`cos(\theta)=\frac{a}{h}`

`a \quad= h*cos(\theta)`
`\qquad= 14 * cos(41)`
`\qquad = 10.57\quad ft`