A bridge is to be constructed over a canyon stretching from point to point as seen in the given figure. A surveyor stands at a point , 30 yards from point , at the edge of the canyon. They measured that , . Work out the length of the bridge.
is a triangle where and . Find the ratio of lengths .
To determine how far a boat is from shore, two radar stations 500 feet apart find the angles out to the boat, as shown in the given figure. Determine the distance of the boat from station and the distance of the boat from shore. Round your answers to the nearest whole foot.
The diagram shows an 8-foot solar panel mounted on the roof of a house. The roof is inclined at to the horizontal, and, for maximum yield, the solar panel is placed at to the horizontal. The solar panel is held in position by a vertical support. How long should the support be to hold the solar panel at an inclination of ? Give your answer to one decimal place.
In triangle , , , and . Determine the length of to the nearest meter.
For the given figure, and . Use the Law of Sines to work out . Give your answer to two decimal places.
is a triangle, where , , and . Find to the nearest tenth of a degree.
is an obtuse-angled triangle at where , and . Find lengths and giving the answer to the nearest integer.
is a triangle where and . Find length giving the answer in terms of .
The diameter of a circle is 82 cm. and are two chords on opposite sides of a circle with lengths 5.1 cm and 48.4 cm respectively. Find the length giving the answer to two decimal places.
is a triangle where and the perimeter is 169 cm. Find the values of and giving the answer to the nearest centimetre.
Which rule could be used to find the length of an unknown side of a triangle, given the measures of two angles and the length of one other side?
Two men are standing in front of a minaret at the points and respectively where the distance between them is 25.4 m. Find the height of the minaret giving the answer to one decimal place.
is a triangle where , and . Find giving the answer to the nearest second.
In the figure .
What is ? Give your answer to two decimal places.
Cities A, B, and C are located such that city A is due west of city B, city C is on a bearing of from city B, and city C is 100 miles from city A and 70 miles from city B. Find the distance between cities A and B giving your answer to one decimal place.
The scale of a map is . The position of three towns on a map form a triangle. Towns B and C are 17 cm apart, and the angles of towns A and B are and respectively. Find the actual distance between towns A and B and between towns A and C giving the answer to the nearest kilometre.
is an equilateral triangle of side length 12 cm that is inscribed in a circle. Find the radius of the circle, giving the answer to two decimal places.
is a right-angled triangle at . The point lies on , where , , and . Find the length of , giving your answer to the nearest centimetre.
Ramy, Shady, and Engy stand at three points, , , and respectively. Suppose that , , and Ramy is exactly 12 feet away from Shady.
Find the distance between Shady and Engy, to two decimal places.
Find the distance between Ramy and Engy, to two decimal places.
is a triangle with a perimeter of 49 cm where the ratio between , and is . Find the length of the smallest side giving the answer to two decimal places.
is a triangle, where , , and length . Find the length of the shortest side of giving the answer to one decimal place.
is a triangle where , and . lies on where . Find the length of giving the answer to two decimal places.
is a triangle where . Find the ratio .
is a triangle where , and . Find the lengths of and giving the answer to one decimal place.