Choosing an appropriate method for finding lengths of a triangle

12 questions

1. In a right triangle, if the hypotenuse is 40 cm and a second side is 32 cm, what is the length of the third side? (Use a calculator to help you.)
2. In a right triangle, if the shortest sides are 10 cm and 7.5 cm, what is the length of the hypotenuse? (Use a calculator to help you.)
3. Would a triangle ABC with sides AB = 9cm, BC = 7.5cm, AC = 12.5cm be similar to the one shown in the diagram?
4. For this pair of triangles, can you determine whether they are similar without using side lengths?
5. In a right triangle, if the hypotenuse is 200 cm and a second side is 120 cm, what is the perimeter? (Use a calculator to help you.)
6. In a right triangle, if the hypotenuse is 30 cm and a second side is 18 cm, what is the area? (Use a calculator to help you.)
7. This robot standing on a box has a fly on the top of their head. How high up (h) is the fly from the ground?
8. This robot standing on a box has an ant on the top of their head. How high up (h) is the ant from the ground to 2 d.p. ?
9. If the area of square ABCD is 25 cm^2, what is the length of the diagonal BD to 2 d.p. ?
10. A rectangle ABCD has length 6cm, and the diagonal angle ABC is 38ᵒ. What is the height of the rectangle to 2 d.p. ?
11. A rectangle ABCD has length 12cm, and the diagonal angle ABC is 40ᵒ. What is the area of the rectangle to 2 d.p. ?
12. Given all angles and the base of an isosceles triangle, what trigonometric function could be used to find the height of the triangle most efficiently?

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