The angle \theta_1θ 1 theta, start subscript, 1, end subscript is located in Quadrant \text{I}Istart text, I, end text, and \cos(\theta_1)=\dfrac{3}{8}cos(θ 1 )= 8 3 cosine, left parenthesis, theta, start subscript, 1, end subscript, right parenthesis, equals, start fraction, 3, divided by, 8, end fraction . What is the value of \sin(\theta_1)sin(θ 1 )sine, left parenthesis, theta, start subscript, 1, end subscript, right parenthesis?

  (√55)/8

Step-by-step explanation:

The sine and cosine are related by ...

  sin² +cos² = 1

Then the sine of the angle is ...

  sin(θ₁) = √(1 -cos(θ₁)²)

  sin(θ₁) = √(1 - (3/8)²) = √(55/64)

  sin(θ₁) = (√55)/8

d. bc = 12 and ef = 16

step-by-step explanation:

we are given that δabc : δdef such that .

also, it is given that

so, from the options, we need that .

a.

b.

c.  

d.

as, we can see that only option d gives the same ratio as i.e. .

hence, the possible lengths are bc = 12 and ef = 16.

3

step-by-step explanation: