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Gennadij [26K]
3 years ago
11

EF is tangent to circle P at G (1,-3). If the slope of EF is 7/9, what is the slope of GP?

Mathematics
1 answer:
pentagon [3]3 years ago
7 0
The center of the circle is at P. 
The tangent EF is tangent to the circle at point G. So GP will be the radius of the circle. 

The slope of tangent EF = 7/9

The tangent of a circle is always perpendicular to the radius at the point where it touches the circle. So we can say that EF is perpendicular to GP.

The product of slopes of two perpendicular line is always equal to -1.

Slope of EF x Slope of GP = -1
So,

Slope of GP = - 1 / (Slope of EF)

Thus slope of GP = - 9/7
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Answer:

101 meters

Step-by-step explanation:

The direct path across the stream and perpendicular to both sides of the stream is one leg of a right triangle. The 20 meter distance on the arriving side of the stream is another leg of the right triangle. The path he actually took is the hypotenuse of the right triangle.

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leg 2 = 20 m

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We have a right triangle, and we know the lengths of the two legs. We need to find the length of the hypotenuse, so we can use the Pythagorean theorem.

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3 years ago
Angle of the Sun A 96-ft tree casts a shadow that is 120 ft long. What is the angle of elevation of the sun
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Answer:

The angle of elevation of the sun is 39⁰

Step-by-step explanation:

Given;

height of the tree, h = 96 ft

length of the shadow, L = 120 ft

                                                   |

                                                   | 96ft

                                                   |

                                                   |

       θ------------------------------------

                    120ft

Completing this triangle to cut across the top of the tree gives you a right angled triangle with θ as the angle of elevation of the sun.

Apply trig-ratio to determine the angle of elevation of the sun;

tanθ = opposite side / adjacent side

tanθ = 96 / 120

tanθ = 0.8

θ = tan⁻¹(0.8)

θ = 38.7⁰

θ = 39⁰

Therefore, the angle of elevation of the sun is 39⁰

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