1. An observer 80 ft above the surface of the water measures an angle of depression of 0.7o to a distant ship. How many miles is the ship from the base of the lighthouse? (5280 ft = 1 mile)

Commercial airliners fly at an altitude of about 10 km. They start descending toward the airport when they are far away, so that they will not have to dive at a steep angle.

2 a) If the pilot wants the plane's path to make an angle of 3o with the ground, at what horizontal distance must the plane start descending?

b) If the pilot starts descending a ground distance of 300 km from the airport, what angle will the plane's path make with the horizontal?

3. A submarine at the surface of the ocean makes an emergency dive, making an angle of 21o with the surface. If it travels for 300 m along a downward path, how deep will it be?

answer: the answer is one of

step-by-step explanation:   we are given to write a proper fraction where the whole is divided into an even number of equal parts less than ten, and an odd number of those parts exist.

an even number less than 10 may be one of 2, 4, 6 or 8. so, the whole may be one of these four evens.

now, an odd number of these parts must exist, so the numerator must be an odd number, one of 1, 3, 5 or 7. it cannot be 9 because then the fraction will become improper.

thus, our fraction may be one of the following

m∠cdf = 43° , m∠gdf = 114°, m∠gde = 23°, m∠edh = 23° , m∠cdh = 157°

step-by-step explanation:

since, it is given that de bisects the angle gdh ⇒ de divides the angle gdh into two equal angles.

⇒ m∠gde = m∠edh

⇒ 8·x   - 1 = 6·x + 5

⇒ x = 3

so, m∠gde = 8·x - 1 = 23°

and m∠edh = 23°

now, it is given ∠cde is an straight angle so, m∠cde = 180°

⇒ m∠cdf + m∠fdg + m∠gde = 180°

⇒ 43° + m∠fdg + 23° = 180°

⇒ m∠fdg = 114°

again, m∠cde = m∠cdh + m∠edh = 180°

m∠cdh + 23° = 180°

⇒ m∠cdh = 157°