Find the area of this isosceles triangle.
Pythagoras’ theorem

Step-by-step explanation:

first you have to divide 16/2 so you can do pythagorus to solve for the height.

16/2=8

√17^2-8^2=15cm - by adding the root symbol we can skip a step.

1/2x16x15=120cm^2

120 cm²

Step-by-step explanation:

The area (A) of a triangle is calculated as

A = bh ( b is the base and h the height )

We require to calculate h

The segment from the vertex to the base is a perpendicular bisector.

This divides the triangle into 2 right triangles, with legs 8 and h and hypotenuse 17.

Using Pythagoras' identity on the left right triangle

The square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is

h² + 8² = 17²

h² + 64 = 289 ( subtract 64 from both sides )

h² = 225 ( take the square root of both sides )

h = = 15, thus

A = 0.5 × 16 × 15 = 8 × 15 = 120 cm²

(sin 42)/31. = sinx)/37

sinx = 37 (sin42)/31

= 37× 0.66/31 = 0.787

x= 51.9

other angle opposite to y = 180-51.9-42

= 180- 93.9 =86.1

so

sin42)/31 = sin 86.1)/y

0.021 = 0.997 /y

y= 0.997/0.021 =47.47