For each of the following:
State the range of possible values of the unknown side as an inequality.
Find the unknown side length, correct to two decimal places.
Find the length of the missing side of the following triangles, rounding your answers to two decimal places when necessary:
Find the size of the missing angle of the following triangles, rounding your answers to two decimal places:
Calculate the length of y in metres, correct to one decimal place:
This triangular prism shaped box below needs a diagonal support inserted from A to F as shown:
If AB = 19, BD = 30 and DF = 43, find the length of AF to two decimal places.
Find the length of AF if AB, BD and DF are increased by 10 \text{ cm}. Round your answer to two decimal places.
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 the radius of the circle, r to one decimal place.
Find the length of BC to the nearest centimetre.
Calculate the area of the following triangles, rounding your answers to two decimal places when necessary:
Find the area of the triangle with side lengths of 5 \text{ cm}, 5 \text{ cm}, and 8 \text{ cm}.
\triangle ABC has an area of 520 \text{ cm}^2. The side BC = 48 \text{ cm} and \angle ACB = 35 \degree:
Find the value of b to the nearest centimetre.
Consider the diagram of an isosceles triangle where h is the height perpendicular to base, b:
Form an expression for h in terms of \theta and a.
Find b in terms of \theta and a.
Form an expression for the area A of the larger triangle, in terms of \theta and a.
The diagram shows a triangular paddock with measurements as shown:
Find the area to the nearest square metre.
Find the area in hectares, rounding your answer to two decimal places.
A triangular-shaped field has sides of length 25 \text{ m}, 29 \text{ m}, and 36 \text{ m}.
Find the area of the field.
Kenneth has been hired to plough the field and to build fencing around its perimeter.
If he charges \$4 per square metre for ploughing and \$7 per metre for fencing, how much does he charge in total?
A boat travels \text{S } 14 \degree \text{E} for 12 \text{ km} and then changes direction to \text{S } 49 \degree \text{E} for another 16 \text{ km}.
Find x, the distance of the boat from its starting point to two decimal places.
Find b to the nearest degree.
Hence, find the bearing that the boat should travel on to return to the starting point.
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 covered by the jet just before levelling out in metres.
If the height of the jet just before levelling off is h \text{ m}, calculate h. Round your answer to the nearest metre.
From the cockpit of an aeroplane flying at an altitude of 3000 \text{ m}, the angle of depression to the airport is 57 \degree. The aeroplane continues to fly in the same straight line, and after a few minutes the angle of depression to the airport becomes 67 \degree.
The horizontal distance between the cockpit at the first sighting and the point directly above the airport is x \text{ m}.
Find the value of x. Round your answer to one decimal place.
The horizontal distance between the cockpit at the second sighting and the point directly above the airport is y \text{ m}.
Find the value of y. Round your answer to one decimal place.
A drone travels due east for 2.2 \text{ km} and then travels on a bearing of \text{S } 32 \degree \text{E} for 5.9 \text{ km}.
Given that the angle of the compass bearing is a \degree, write the compass bearing needed to return to the starting point, in terms of a.
Find x, the distance between the end point to the start point of the drone's flight. Round your answer to two decimal places.
Hence, find a to the nearest degree.
An industrial site in the shape of a triangle is to take up the space between where three roads intersect.
Calculate the area of the site. Round your answer to two decimal places.
The Bermuda triangle is an area in the Atlantic Ocean where many planes and ships have mysteriously disappeared. Its vertices are at Bermuda \left(B\right), Miami \left(M\right) and Puerto Rico \left(P\right).
Find the size of \angle BMP to the nearest minute.
Find the area taken up by the Bermuda Triangle, correct to two decimal places.
