6.06 Problem solving with trigonometry
Consider the diagram shown:
Find the length of AB, correct to two decimal places.
Consider the following diagram:
Find the length of AD to two decimal places.
Consider the following diagram:
Find the length of AD to two decimal places.
Consider the following diagram:
Find the values of x and h to the nearest whole number.
For each of the following diagrams.:
Find y, correct to two decimal places.
Find w, correct to two decimal places.
Hence, find the value of x, correct to one decimal place.
Consider the given diagram:
Find the length of CD, to one decimal place.
AB is a tangent to a circle with centre O.
OB is 24 \text{ cm} long and cuts the circle at C.
Find the length of BC to the nearest centimetre.
Consider the following diagram:
Find the value of k. Round your answer to two decimal places.
In the following diagram, \angle CAE = 61 \degree, \angle CBE = 73 \degree and CE = 25.
Find the length of AB, correct to two decimal places.
Find the length of BD, correct to one decimal place.
Consider the given figure:
Find x, correct to two decimal places.
Find y, correct to two decimal places.
Find z, correct to two decimal places.
An isosceles triangle has equal side lengths of 10 \text{ cm} and a base of 8 \text{ cm} as shown.
Calculate the size of angle A to one decimal place.
Consider the following figure:
Find the size of angle x in degrees, correct to two decimal places.
Find the size of angle y in degrees, correct to two decimal places.
Two flag posts of height 12 m and 17 m are erected 20 m apart.
Find the length, l, of the string needed to join the tops of the two posts. Round your answer to one decimal place.
A jet takes off and leaves the runway at an angle of 34 \degree. It continues to fly in this direction for 7 \text{ min} at a speed of 630 \text{ km/h} before levelling out.
Find the distance in metres covered by the jet just before levelling out.
If the height of the jet just before levelling out is h \text{ m}, calculate h to the nearest metre.
A helicopter is flying at an altitude of 198 \text{ m}. Its landing pad is at an angle of depression of 44 \degree.
Determine the distance, d, between the helicopter and the landing pad. Round your answer to the nearest whole number.
A suspension bridge is being built. The top of the concrete tower is 35.5 \text{ m} above the bridge and the connection point for the main cable is 65.9 \text{ m} from the tower.
Assume that the concrete tower and the bridge are perpendicular to each other.
Find the length of the cable to two decimal places.
Find the angle the cable makes with the road to two decimal places.
A sand pile has an angle of 40 \degree and is 10.6 \text{ m} wide.
Find the height of the sand pile, h, to one decimal place.
A girl is flying a kite that is attached to the end of a 23.4 \text{ m} length of string. The angle between the string and the vertical is 21\degree. If the girl is holding the string 2.1 \text{ m} above the ground:
Find x, correct to two decimal places.
Hence find the height h of the kite above the ground, correct to two decimal places.
Mae observes a tower at an angle of elevation of 12 \degree. The tower is perpendicular to the ground. Walking 67 \text{ m} towards the tower, she finds that the angle of elevation increases to 35 \degree as shown in the diagram below:
Let x be the length of BC .
Use triangle BCD to create an expression for h in terms of x.
Use triangle ACD to create an expression for h in terms of x.
Use the answers from parts (a) and (b) to determine the value of x. Give your answer to one decimal place.
Hence, solve for h, the height of the tower. Give your answer to one decimal place.
Determine the length of a. Give your answer to two decimal places.
A safety fence is constructed to protect tourists from the danger of an eroding castle toppling down. The surveyor takes an angle measurement to the top of the tower of 10 \degree. She then walks 29 \text{ m} towards the tower and takes another reading of 22 \degree.
Find the value of h to the nearest metre.
