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Worksheet: Trigonometry: Mixed Practice

Q1:

Find the length of , given that , , and .

  • A cm
  • B cm
  • C cm
  • D cm
  • E cm

Q2:

A palm tree 10.6 metres tall is observed from a point 12 metres away on the same horizontal plane as the base of the tree. Find the angle of elevation to the top of the palm tree giving the answer to the nearest minute.

  • A
  • B
  • C
  • D

Q3:

Find the area of triangle , given that , , and .

Q4:

is an isosceles triangle where and . Find the value of given lies on the midpoint of where .

  • A
  • B
  • C
  • D

Q5:

A chord is drawn in a circle whose radius is 8 cm. If the size of its central angle is , calculate the length of the chord to the nearest thousandth.

  • A10.285 cm
  • B15.757 cm
  • C12.257 cm
  • D16.000 cm
  • E6.128 cm

Q6:

is a rhombus where the lengths of the diagonals and are 14.2 cm and 23.2 cm respectively. Find giving the answer to the nearest second.

  • A
  • B
  • C
  • D
  • E

Q7:

From the top of a house 15 m tall, the angles of elevation and depression of the top and the base of a building are and respectively. Find the height of the building giving the answer to the nearest metre.

Q8:

is a triangle where , , and . Point lies on where . Find the area of giving the answer to two decimal places.

Q9:

is a triangle where , , and . Point lies on where . Find the area of giving the answer to two decimal places.

Q10:

Find the value of .

  • A
  • B
  • C
  • D
  • E

Q11:

is a trapezoid-shaped piece of land where is parallel to and . Find given that , , and . Give the answer to the nearest second.

  • A
  • B
  • C
  • D

Q12:

The dimensions of a rectangular garden is 20 meters by 17 meters. Triangle represents the lawn where . Find the value of giving the answer to the nearest second.

  • A
  • B
  • C
  • D

Q13:

Find the lengths of and given is a right triangle at where and . Give the answers to the nearest centimeter.

  • A,
  • B,
  • C,
  • D,

Q14:

Two boys are on opposite sides of a tower. They see the top of the tower at angles of elevation and , respectively. If the height of the tower is 21 m, find the distance between the two boys to the nearest meter.

Q15:

In the given figure, , , and . Calculate the length of . Give your answer to two decimal places.

Q16:

In the given figure, , , and . Calculate the length of . Give your answer to two decimal places.

Q17:

Robert wants to find the height of an oak tree in his garden. He decides he needs to make a clinometer in order to measure the angle of elevation. He uses a straw, a protractor, some string, and a bit of Blu-Tack as a weight. Robert stands at a perpendicular distance of 85 ft from the base of the tree and measures the angle on his clinometer to be as seen in the diagram. Given that Robert’s eyeline is 6 ft from the ground, work out the height of the tree to the nearest foot.