Mixed Trig Problems

For each problem show a complete solution with diagrams that include all the pertinent facts and answers.

In ∆𝐴𝐵𝐶, cos 𝐴 = −0.6.

Find sin A and tan A.

In ∆𝐴𝐵𝐶, cos 𝐴 = −0.6. Find sin A and tan A.

Sin A= 0.8, tan A=-𝟒

𝟑

Show a complete solution with diagrams that include all the pertinent facts and answers.

A submarine dives at an angle of 16 degrees with the horizontal. If it takes 4 min to dive from the surface to a depth of 300 ft, how fast does it move along its sloping path downward? Give your answer in feet per minute. Then convert it to nautical miles per hour. (1 nautical mile per hour = 6080 feet per hour)

Show a complete solution with diagrams that include all the pertinent facts and answers.

A submarine dives at an angle of 16 degrees with the horizontal. If it takes 4 min for the Sub to dive from the surface to a depth of 300 ft, how fast does the Sub move along its sloping path downward? Give your answer in feet per minute. Then convert it to nautical miles per hour. (1 nautical mile per hour = 6080 feet per hour)

272 ft/min, 2.69 knots Show a complete solution with diagrams that include all the pertinent facts

and answers.

In parallelogram ABCD:

∠𝐴 = 60°, AB = 5, and AD = 8. a) Find the area of ABCD.

b) Find the lengths of both diagonals.

Show a complete solution with diagrams that include all the pertinent facts and answers.

In parallelogram ABCD, ∠𝐴 = 60 𝑑𝑒𝑔𝑟𝑒𝑒𝑠, AB = 5, and AD = 8.

a) Find the area of ABCD. 20 𝟑 𝒐𝒓 𝟑𝟒. 𝟔𝟒𝟏

b) Find the lengths of both diagonals.

7, 𝟏𝟐𝟗

Show a complete solution with diagrams that include all the pertinent facts and answers.

The diagonals of a parallelogram have lengths 8 and 14 and they meet at a 60 degree angle. Find the area and the perimeter of the parallelogram.

Show a complete solution with diagrams that include all the pertinent facts and answers.

The diagonals of a parallelogram have lengths 8 and 14 and they meet at a 60 degree angle. Find the area and the perimeter of the parallelogram.

Area = 28 𝟑 or 48.497

Perimeter = 2 𝟑𝟕+ 2 𝟗𝟑 or 31.452

Show a complete solution with diagrams that include all the pertinent facts and answers.

The perimeter of a regular decagon (10 sides) is 240. Find its area.

Show a complete solution with diagrams that include all the pertinent facts and answers.

The perimeter of a regular decagon (10 sides) is 240. Find its area.

≈ 𝟒𝟒𝟑𝟎

Show a complete solution with diagrams that include all the pertinent facts and answers.

If fencing costs $2.50 per foot, how much will it cost to buy fencing to go around the plot of land shown below?

128⁰

50 ft

30 ft

Show a complete solution with diagrams that include all the pertinent facts and answers.

If fencing costs $2.50 per foot, how much will it cost to buy fencing to go around the plot of land shown below?

128⁰

50 ft

30 ft

$478.77

Show a complete solution with diagrams that include all the pertinent facts and answers.

In the township of Madison, rural undeveloped land is taxed at a rate of $115 per acre. Find the tax on the plot of land shown below. (1 acre = 43,560 square feet)

125 ft 100 ft

130 ft

80⁰

120⁰

Show a complete solution with diagrams that include all the pertinent facts and answers.

In the township of Madison, rural undeveloped land is taxed at a rate of $115 per acre. Find the tax on the plot of land shown below. (1 acre = 43,560 square feet)

125 ft 100 ft

130 ft

80⁰

120⁰

$41.63 Show a complete solution with diagrams that include all the pertinent facts

and answers.

A ship is steaming north at 6 knots (6 nautical miles per hour) when the captain sights a small island at an angle of 15 degrees to the east of the ship’s course, as shown below. After 10 min, the angle is 28 degrees. How far away is the island at this moment?

28⁰

15⁰

N

Show a complete solution with diagrams that include all

the pertinent facts and answers.

A ship is steaming north at 6 knots (6 nautical miles per hour) when the captain sights a small island at an angle of 15 degrees to the east of the ship’s course, as shown below. After 10 min, the angle is 28 degrees. How far away is the island at this moment?

28⁰

15⁰

N

1.15 Nautical mi ≈1.32 mi

Show a complete

solution with diagrams that include all the pertinent facts and answers.

An airplane at A is flying at a height of 6 mi above Earth’s surface at S, shown below.

a) Find the distance to the nearest tenth of a mile from A to the horizon H. (Earth’s radius is about 4000 mi)

b) Find the curved distance to the nearest tenth of a mile from S along Earth’s surface to H.

C

4000 mi

S

6 mi Point A

H Show a

complete solution with diagrams that include all the pertinent facts and answers.

An airplane at A is flying at a height of 6 mi above Earth’s surface at S, shown below.

a) Find the distance to the nearest tenth of a mile from A to the horizon H. (Earth’s radius is about 4000 mi)

b) Find the curved distance to the nearest tenth of a mile from S along Earth’s surface to H.

C

4000 mi

S

6 mi Point A

H

219.2 mi

219.0 mi

Show a complete

solution with diagrams that include all the pertinent facts and answers.

1. Find the value of x. 2. Solve all three triangles.

Show a complete solution with diagrams that include all the pertinent facts and answers.