Question

((50 points Plus Brainliest if answered correctly))
5. Find two angles that satisfy the equation sin(4x + 14)º = cos(–3x + 73)º. *

26º and 74º
29º and 61º
64º and 116º
26º and 64º

10. An eagle 300 feet in the air spots its prey on the ground. The angle of depression to its prey is 15°. What is the horizontal distance between the eagle and its prey? Round to the nearest foot.

1120 ft
1159 ft
310 ft
723 ft

Answer 1

Answer:

Step-by-step explanation:

9.

sin x=cos y

x+y=90

4x+14+(-3x+73)=90

4x+14-3x+73=90

x+87=90

x=90-87=3

4x+14=4(3)+14=12+14=26

x=26°

y=90-26=64°

angles are 26°,64°

10.

let horizontal distance=x

$\frac{300}{x} =tan15\\\frac{x}{300} =cot~15=cot(90-75)=tan 75\\x=300 \times ~\tan ~75 \approx 1119.62 \approx 1120~ft$

Answer 2

[5] Find two angles that satisfy the equation sin(4x + 14)º = cos(–3x + 73)º. *

Answer:

$26$° $and$ $64$°

Step-by-step explanation:

$sin$ $x = cos$ $y$

$x+y=90$

$4x+14+(-3x+73)=90$

$4x+14-3x+73=90$

$x+87=90$

$x=90-87=3$

$4x+14=4(3)+14=12+14=26$

$x=26$°

$y=90-26=64$°

$Hence,$ $Answer$ $is$ $26$° $and$ $64$ °

[10] An eagle 300 feet in the air spots its prey on the ground. The angle of depression to its prey is 15°. What is the horizontal distance between the eagle and its prey? Round to the nearest foot.

Answer:

$1120 ft$

Step-by-step explanation:

$d =distance$

$tan(15)=300/d$

$d=300/tan(15)$

$d=1119.6ft=1120ft$