Answer:
1: x=20, y=20√2
5: x=8, y=4
6: x= 10, y=10√3
Step-by-step explanation:
In question 1:
This triangle is a 45-45-90º triangles. Triangles such as these have known proportions of side lengths: each of the two 'legs' are equivalent, and the hypotenuse is √2 times longer than the leg.
In this question, one leg is 20. The other leg, indicated by 'x', will also be 20. The hypotenuse, 'y', will be 20√2.
In question 5:
This triangle is a 30-60-90 triangle. These also have known side lengths: the hypotenuse is twice as long as the shortest leg, and the middle-lengthed leg of the triangle will be √3 times as long as the shortest leg.
In this scenario, the middle leg is 4√3, and you can calculate that the shortest leg, 'y', will be 4. Using that, the hypotenuse, 'x', is twice as long as the shortest leg, so x is 8.
In question 6:
This is also a 30-60-90 triangle.
In this one, the hypotenuse is 20, and so, the shortest leg, 'x', will be half of 20, being 10. Now, as the shortest leg is 10, the middle leg, 'y', will be √3 times longer than 10, which is 10√3.
