1. y=12.6 units
2. x=25.30 units
3. x=5.70 units, y=11.50 units
4. x=4.10 units, y=11.50 units.
Step-by-step explanation:
In all cases, apply the Pythagorean relationship where the sum of the squares of the sides equals the square of the hypotenuse.
a²+b²=c² where a and b are the sides, and c is the hypotenuse
1.
In this question;
First find b, where c=5 and a is 4
a²+b²=c²
4²+b²=5²
16+b²=25
b²=25-16=9
b=√9=3 units
To get y apply the formula now where c=13 and b=3
y²+3²=13²
y²+9=169
y²=169-9=160
y=√160=12.6 units.
2.
The triangle with a hypotenuse of 20 in is a right-isosceles triangle.
In this triangle apply the sine of an angle law to get the height of the triangle where the angle is 45°
Sin 45°=opposite side length/hypotenuse length
sin 45°=h/20
h=20*sin 45°=14.10 units
Use the height to find the side length for the small triangle when now c=18 and b=14.10
a²+b²=c²
a²+14.10²=18²
a²=18²-14.10²
a²=11.20
Now x= 11.20+14.10 =25.30 units
3.
In this case first find length of x given b=4 and c=7
a²+b²=c²
x²+4²=7²
x²+16=49
x²=49-16
x²=33
x=√33 =5.70 units
Now find y using a=x=5.70 and b=6+4=10
a²+b²=c²
5.70²+10²=c²
132.49=c²
√132.49=c
11.50=c=y
y= 11.50 units
4.
First find x where b=8 and c=9
x²+8²=9²
x²=9²-8²
x²=17
x=√17 =4.10 units
Now find y where b=8, a=(4.10+4.10)=8.20 ----because you have two equal sides
a²+b²=c²
8.20²+8²=y²
131.24=y²
√131.24=y
11.50 units = y
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Pythagorean relationship application:https://brainly.com/question/9319790
Keywords: calculate, unknown sides, tenth
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