SOLUTION: Q1. The area of this isosceles triangle is 15cm squared. The angle ABC is 24 degrees. Work out both lengths correct to 1 decimal place. Q2. This isosceles triangle as sides of l

Question 729425: Q1. The area of this isosceles triangle is 15cm squared. The angle ABC is 24 degrees. Work out both lengths correct to 1 decimal place.
Q2. This isosceles triangle as sides of length 5.7cm and area 4cm squared. The diagram shows that there are 2 possible answers for the angle x. Work out both angles correct to 1 decimal place.
Please help, i will need them for Wednesday 27th March. thankyou
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
Q1. If B is the vertex, the point where the two equal length sides meet, the altitude to the vertex,splits the triangle into two congruent right triangles.
Half the length of base AC is . The length of altitude BP is the height and the area of the triangle is

The measures of angles ABP and CBP are the same, and half of the measure of ABC, meaning

The trigonometric ratios, applied to ABP tell us that
-->
-->
So --> --> --> --> --> cm rounded to
--> --> (rounded
and rounded to

Alternatively, we could have used the fact that the area of a triangle can be calculated as
and since , then the area is
--> -->

Q2. Using the same drawing, the length of both legs of the isosceles triangle (AB and BC) is the same, .
As above the area of the triangle can be calculated as
and since , then the area is , so
--> --> (rounded)
Since it could be that angle ABC measures , which would make the measure of APB
and the measure of CBA .
Then the base angles would be and the vertex angle would be

However, the right triangles could be reversed, with a base angle CBA measuring } and ABP measuring for a vertex angle measuring} which also has
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