Answer
The value of x = 8 in.
y = 8√2 = 11.31 in.
For the second question,
x = 8.3 units
Explanation
Isoscelles triangles have two of their sides being of the same lengths and those two sides are the ones whose base angles are the same.
From the image, we can see that two angles of the triangle have the same measures, hence, we can easily conclude that
x = 8 inches.
To find y, we will use pythagoras theorem.
The Pythagorean Theorem is used for right angled triangle, that is, triangles that have one of their angles equal to 90 degrees.
The side of the triangle that is directly opposite the right angle or 90 degrees is called the hypotenuse. It is normally the longest side of the right angle triangle.
The Pythagoras theorem thus states that the sum of the squares of each of the respective other sides of a right angled triangle is equal to the square of the hypotenuse. In mathematical terms, if the two other sides are a and b respectively,
a² + b² = (hyp)²
For this triangle,
hyp = y
a = 8 in
b = x = 8 in
a² + b² = (hyp)²
8² + 8² = y²
64 + 64 = y²
y² = 128
Take the square roots of both sides
√(y²) = √128
y = 8√2 = 11.31 in
For the other question.
In a right angle triangle, the side opposite the right angle is the Hypotenuse, the side opposite the given angle that is non-right angle is the Opposite and the remaining side is the Adjacent.
For that triangle,
Hyp = 11 units
Opp = ?
Adj = x
θ = 41°
We can then use trignometrical identities to solve this
CAH allows us to say
Cos 41° = (Adj/Hyp)
Cos 41° = (x/11)
x = 11 Cos 41°
x = 11 (0.7547)
x = 8.3 units
Hope this Helps!!!
