Answer:
6.4 = b and 7.8 = a
Explanation:
Using the formula:
a^2 + b^2 = c^2
we can find the length of b
for the first triangle
now we just plug in the lengths.
5^2 + 4^2 = b^2
simplify into :
25 + 16 = b^2
add
41 = b^2
now in order to get rid of the ^2, we just find the square root of 41.
√41 ≈ 6.4
6.4 = b
Now we just need to solve for A
since we know
a^2 + b^2 = c^2 that must mean
c^2 - b^2 = a^2
so this is the formula we will be using.
now we just plug in the lengths of the second triangle into this equation.
10.5^2 - 7^2 = a^2
simplifies into
110.25 - 49 = a^2
subtract
61.25 = a^2
now we just find the square root of 61.25.
√61.25 = 7.8
7.8 = a
you can check this by putting it back in the formula
a^2 + b^2 = c^2
I will do this quickly (only for the second triangle)
we know
a = 7.8
b = 7
c = 10.5
7.8^2 + 7^2 = 10.5^2
simplifys into
60.84 + 49 = 110.25
60.84 + 49 ≈ 110
110.25 ≈ 110
110 = 110
which proves that this is correct.