What is the circumference of 42 in a circle?

An observer (O) spots a bird flying at a 55° angle from a line drawn horizontal to its nest. If the distance from the observer (

kolezko [41]

Answer:

x = 18311.61 m

Step-by-step explanation:

It is given that, An observer (O) spots a bird flying at a 55° angle from a line drawn horizontal to its nest. The distance from the observer (O) to the bird (B) is 15,000 ft. We need to find the distance between the bird and the nest. It is based on trigonometry. So,

$\sin (35)=\dfrac{\text{opposite}}{\text{hypotenuse}}$

Let x is the distance between the bird and the nest

So,

$\sin (55)=\dfrac{15000}{x}\\\\x=\dfrac{15000}{ \sin(55)} \\\\x=18311.61\ m$

So, the distance between the bird and the nest is 18311.61 m.

7 0

3 years ago

Help on 9 & 10 please!

Mandarinka [93]

Step-by-step explanation:

9. x and z are equal. y+z=90

148-x=180 x+148 are supplementary

-148 -148 Subtract 148 from both sides to isolate x

x=32 degrees

z=32 degrees b/c x and z are equal

y+z=90 y and z are complementary

y+(32)=90 Substitute 32 in for z

-32 -32

y =58 degrees

10. (4x-25)=(2x+7) B/c of the bisection, the two angles are equal.

4x-25 =2x+7 Remove parenthesis

-2x -2x Subtract 2x from both sides

2x-25 = +7

+25 +25 Add 25 to both sides to isolate x

2x = 32

/2 /2 Divide both sides by 2 to isolate x

x = 16

(4(16)-25)+(2(16)+7)=78 degrees Substitute 16 into the equation, this time adding the values instead of setting them equal to get the angle measure requested.

11. (6x-47)+(x+4)=90 Angles that are complementary add up to 90 degrees

7x-43 =90 Add like terms

+43 +43 Add 43 to both sides to isolate x

7x =133

/7 /7 Divide both sides by 7 to isolate x

x =19

((19)+4)=23 degrees Substitute x into the angle measure requested

12. 180=2x-9+x Use the words to help you determine what each value is.

180=3x-9 Add like terms

+9 +9 Add 9 to both sides to isolate x

189=3x

/3 /3 Divide both sides by 3 to isolate x