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;

$x=\sqrt{75}$

$\Rightarrow x=5\sqrt{3}yds$

QUESTION 2

$\sin(a)=\frac{Opposite}{Hypotenuse}$

$\sin(a)=\frac{5\sqrt{3}}{14}$

$\cos(a)=\frac{Adjacent}{Hypotenuse}$

$\cos(a)=\frac{11}{14}$

$\tan(a)=\frac{Opposite}{Adjacent}$

$\tan(a)=\frac{5\sqrt{3}}{11}$

$\sin(b)=\frac{Opposite}{Hypotenuse}$

$\sin(b)=\frac{11}{14}$

$\cos(b)=\frac{Adjacent}{Hypotenuse}$

$\cos(b)=\frac{5\sqrt{3}}{14}$

$\tan(b)=\frac{Opposite}{Adjacent}$

$\tan(b)=\frac{11}{5\sqrt{3}}$

Rationalize the denominator to get;

$\tan(b)=\frac{11\sqrt{3}}{15}$

Answer 2

Answer:

1) $x=5\sqrt{3}$

2) $sin(a)=5\sqrt{3}/14$

$sin(b)=11/14$

$cos(a)=11/14$

$cos(b)=5\sqrt{3}/14$

$tan(a)=5\sqrt{3}/11$

$tan(b)=11/5\sqrt{3}$

Step-by-step 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:

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

MEASURE OF ANGLE:

Keep the identities on mind:

$sin\alpha=opposite/hypotenuse$

$cos\alpha=adjacent/hypotenuse$

$tan\alpha=opposite/adjacent$

Susbstitute values, then:

$sin(a)=5\sqrt{3}/14$

$sin(b)=11/14$

$cos(a)=11/14$

$cos(b)=5\sqrt{3}/14$

$tan(a)=5\sqrt{3}/11$

$tan(b)=11/5\sqrt{3}$