Question

use the pythagorean theorem to find the missing side length. 2 write sin, cosine, tangent of each angel.​

Answer 1

QUESTION 1

The missing side length is
`x`.

From the Pythagoras Theorem;

`x^2+11^2=14^2`

This implies that;

`x^2+121=196`

`x^2=196-121`

`x^2=75`

Take positive square root of both sides;

`x=√(75)`

`\Rightarrow x=5√(3)yds`

QUESTION 2

`\sin(a)=(Opposite)/(Hypotenuse)`

`\sin(a)=(5√(3))/(14)`

`\cos(a)=(Adjacent)/(Hypotenuse)`

`\cos(a)=(11)/(14)`

`\tan(a)=(Opposite)/(Adjacent)`

`\tan(a)=(5√(3))/(11)`

`\sin(b)=(Opposite)/(Hypotenuse)`

`\sin(b)=(11)/(14)`

`\cos(b)=(Adjacent)/(Hypotenuse)`

`\cos(b)=(5√(3))/(14)`

`\tan(b)=(Opposite)/(Adjacent)`

`\tan(b)=(11)/(5√(3))`

Rationalize the denominator to get;

`\tan(b)=(11√(3))/(15)`

Answer 2

1)
`x=5√(3)`

2)
`sin(a)=5√(3)/14`

`sin(b)=11/14`

`cos(a)=11/14`

`cos(b)=5√(3)/14`

`tan(a)=5√(3)/11`

`tan(b)=11/5√(3)`

Explanation:

The Pythagorean Theorem is:

`a^(2)=b^(2)+c^(2)`

Where a is the hypotenuse and b and c are the legs.

The missing side lenght is one of the legs, then you must solve for one of them. Therefore, this is:

`x=\sqrt{(14yd)^(2)-(11yd)^(2)}=5√(3)yd`

MEASURE OF ANGLE:

Keep the identities on mind:

`sin\alpha=opposite/hypotenuse`

`cos\alpha=adjacent/hypotenuse`

`tan\alpha=opposite/adjacent`

Susbstitute values, then:

`sin(a)=5√(3)/14`

`sin(b)=11/14`

`cos(a)=11/14`

`cos(b)=5√(3)/14`

`tan(a)=5√(3)/11`

`tan(b)=11/5√(3)`