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In this lesson, we will learn how to find an angle using the sine and cosine ratios.

Q1:

Find the value of π giving the answer in radians to two decimal places.

Q2:

A builder leans a 5-foot plank of wood against a vertical wall. If one end of the plank is 3 feet from the bottom of the wall, what is the angle between the plank and the wall?

Q3:

The base of a truck is 2 feet off the ground and a 20-foot ramp is used to load the truck. Find, to two decimal places, the angle the ramp makes with the horizontal ground.

Q4:

In the given figure, π΅ π΄ has been extended to the point π· such that π΅ π· and π· πΆ are perpendicular.

Work out the value of s i n 1 1 0 to 4 decimal places.

Work out the value of s i n 7 0 to 4 decimal places.

Work out the length of π· πΆ to 2 decimal places.

Work out the area of the triangle π΄ π΅ πΆ to 2 decimal places.

Q5:

A circle has a radius of 16 cm. A chord is drawn where the central angle is 8 0 β . Find the length of the chord giving the answer to three decimal places.

Q6:

In the given figure, π β π΅ π΄ πΆ = 9 0 β and π΄ π· β₯ π΅ πΆ . What is π΄ πΆ π s i n ?

Q7:

Find the measure of β π΅ , given π΄ π΅ πΆ π· is an isosceles trapezium where π΄ π΅ = π΄ π· = π· πΆ = 1 3 c m and π΅ πΆ = 1 7 c m giving the answer to the nearest second.

Q8:

Find the measure of β π΅ , given π΄ π΅ πΆ π· is an isosceles trapezium where π΄ π΅ = π΄ π· = π· πΆ = 7 c m and π΅ πΆ = 9 c m giving the answer to the nearest second.

Q9:

In the given figure, π΄ πΆ = 5 , π΅ πΆ = 7 , and π β π΅ πΆ π΄ = 4 1 β .

Calculate the height π΄ π· to 2 decimal places.

Calculate the area of the triangle π΄ π΅ πΆ to 2 decimal places.

Q10:

Find s i n π΄ given π΄ π΅ πΆ is a right-angled triangle at π΅ where the point π· lies on π΅ πΆ , π· πΈ is perpendicular to π΄ πΆ , π· πΈ = 1 8 c m and πΆ πΈ = 2 4 c m .

Q11:

A 33 ft ladder leans against a building such that the angle between the ground and the ladder is 8 0 β . How high does the ladder reach up the side of the building?

Q12:

The distance between two villages π΄ and π΅ is 13 km where π΄ is west of π΅ . Village πΆ is located 3 7 β east of north of π΄ and 4 8 β north of west of π΅ . Find the distance between π΅ and πΆ giving the answer to the nearest kilometre.

Q13:

The base of a truck is 2 feet off the ground and a 15-foot ramp is used to load the truck. Find the angle the ramp makes with the horizontal ground.

Q14:

π΄ , π΅ , and πΆ are three towns that lie in the same horizontal plane. π΅ lies 38 km southwest of π΄ . π΄ lies 2 3 β east of north of πΆ and π΅ lies 7 β east of north of πΆ . Find the length of π΄ πΆ giving the answer to the nearest kilometre.

Q15:

In the given figure, π β π΅ π΄ πΆ = 9 0 β and π΄ π· β₯ π΅ πΆ . What is π΅ πΆ π s i n ?

Q16:

π΄ π΅ πΆ is a right-angled triangle at π΅ where π β πΆ = 6 5 4 8 β² β and π΄ πΆ = 1 2 c m . Find the length of π΄ π΅ giving the answer to two decimal places.

Q17:

Find the value of s i n s i n π + π given π π π is a right-angled triangle at π , π π = 5 8 c m , π π = 4 0 c m and π π = 4 2 c m .

Q18:

In the given figure, π΄ π΅ = 6 , π΅ πΆ = 1 1 , and π β π΄ π΅ πΆ = 6 1 β .

Q19:

In the given figure, π΄ πΆ = 5 , π΅ πΆ = 7 , and π β π΅ πΆ π΄ = 4 1 β . Work out the height π΄ π· of the triangle to 2 decimal places.

Q20:

Find s i n π΄ , given π΄ π΅ πΆ is a right-angled triangle at πΆ where π΄ π΅ = 2 0 c m and π΅ πΆ = 1 6 c m .

Q21:

A mountain has a uniform incline of 2 8 β . If a person walks 127 metres to the peak of the mountain, how tall is the mountain? Give the answer to the nearest metre.

Q22:

What is the value of s i n π in the given triangle?

Q23:

Find the area of the triangle π΄ π΅ πΆ given π΄ π΅ = π΄ πΆ = 2 1 c m and π΅ πΆ = 2 0 c m . Give the answer to two decimal places.

Q24:

Find π β π΅ π΄ πΆ giving the answer to the nearest second.

Q25:

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