Answer:
The lengths of the other two sides are 2.33 units and 5.52 units
Step-by-step explanation:
Since we have three angles of a triangle given and a side, we use the sine rule to find the other two sides.
Given that the angles are 25, 90 and 65 respectively and the side adjacent to the 25 angle is 5 units. The side opposite to the 65 angle is also the 5 unit side and the side opposite to the 25 angle is the side adjacent to the 65 side, let it be "a" and, since we have a 90 angle, it is a right angled triangle.
So, using the sine rule, a/sin25 = 5/sin65
a = 5sin25/sin65
a = 5 × 0.4226/0.9063
a = 2.113/0.9063
a = 2.331
a ≅ 2.33 units long
We now find the side opposite the right angle by using Pythagoras' theorem. Let that side be "b".
So, b² = a² + 5²
b² = 2.33² + 5²
b²= 5.4289 + 25
b² = 30.4289
taking square-root of both sides, we have
√b² = √30.4289
b = 5.516
b ≅ 5.52 units long
So, the lengths of the other two sides are 2.33 units and 5.52 units