Question

Pls help, question on picture, will do brainliest if right no links!!!!!

Answer 1

Answer:

$\boxed {\boxed {\sf sin(\theta)=\frac {16}{20}}}$

Step-by-step explanation:

We are asked to find the sine for the angle indicated. Remember that sine is equal to the opposite over the hypotenuse.

• sin(θ)= opposite/hypotenuse

Analyze the triangle given. We have the 2 legs (16 and 12), but we do not have the hypotenuse (the longest side). We must solve for it.

Since this is a right triangle, we can use the Pythagorean Theorem.

$a^2+b^2=c^2$

Where a and b are the legs and c is the hypotenuse. We know 16 and 12 are the legs.

$(16)^2+(12)^2=c^2$

Solve the exponents.

• 16²= 16*16=256
• 12²= 12*12= 144

$256+144=c^2$

$400=c^2$

Since we are solving for c, we must isolate the variable. It is being squared, so we take the inverse: a square root.

$\sqrt{400}=\sqrt{c^2} \\20=c$

Now we know the hypotenuse is 20. The side opposite of the angle θ is 16.

• opposite= 16
• hypotenuse=20

$sin (\theta)= \frac {opposite}{hypotenuse} \\sin (\theta)= \frac{16}{20}$

The sine of the angle is equal to 16/20. This can be reduced to 4/5 if necessary (by dividing the numerator and denominator by 4).

Answer 2

Sin = opposite/hypothenuse
Given opposite = 16
Hypothenuse = ?
Use Pythagorean theorem to find hypothenuse

12^2 + 16^2 = h^2
144 + 256 = h^2
h^2 = 400, h = 20

You know hypothenuse is 20
Opposite/hypothenuse

Solution: 16/20
Simplify if you need to (4/5)