please help in 10th grade

Question

4.<AB is right angle. BX bisects < ABC. Find x if m<ABX= 2x-3?

5. Tell whether the lengths 8, 14, and 10 form the sides of an acute, right, obtuse, or not a triangle?

6. In the triangle, LJ= 9 and m<L= 40 find LR.

7. The legs of a triangle are 4 and 7, what is the length of the hypotenuse?

Answer 1

5). The lengths 8, 14, and 10.

Check by using Pythagorean theorem.

If c² = a² + b², then it is a right angle.

If c² < a² + b², then it is a acute angle.

If c² > a² + b², then it is a obtuse angle.

Here a = 8, b = 10, and c = 14

a² = 8² = 64, b² = 10² = 100, and c² = 14² = 196.

By checking a² + b² = 64 + 100 = 164, c² = 14² = 196.

a² + b² < c² so, it is a obtuse angle.

Answer 2

7). The legs of a triangle are 4 and 7.

Pythagoras' Theorem tells us:

The square of the hypotenuse is equal to the sum of the squares of the two shorter sides.

The hypotenuse is h² = 4² + 7²

h² = 16 + 49 = 65

Apply square root each side.

h = √65 = 8.062.