Step-by-step explanation:
Pythagoras formula for the relation of the side lengths in a right-angled triangle :
c² = a² + b²
c is the Hypotenuse, the side opposite of the 90 degree angle.
a and b are the "legs".
3.
c² = 10² + 21² = 100 + 441 = 541
c = sqrt(541) = 23.2594066...in
so, none of the provided answers. are you sure you put the right numbers ? maybe the second leg is sqrt(21) instead of 21 ? because then it would be
c² = 10² + sqrt(21)² = 100 + 21 = 121
c = 11in
4.
10² = a² + 6²
100 = a² + 36
64 = a²
a = 8 m
5.
again, there must be something wrong. the height of the triangle cannot be longer than the legs of the triangle.
given the answer options of 5 - 9 cm it cannot be 32cm. maybe you mean 3.2 cm ?
also interesting that it says "attitudes" - plural. what do you mean by that ?
because there is something else missing. like how long are the segments of the Hypotenuse where the height (or altitude) is touching the Hypotenuse ?
with just the Hypotenuse length and the height length we cannot calculate the other parts of the triangle, because we can move the height freely along the Hypotenuse and draw fitting right-angled triangles on that "skeleton".
6.
similar triangles. that means the lengths of corresponding lines (like sides or heights) are all in relation with the same scaling factor.
so, the small triangle has its "height" side of 1 ft, and multiplying with the scaling factor would then give us the height of the flag pole.
what is the scaling factor ? we get that from the pair of corresponding sides we already know : the shadows.
going from the small to the large triangle we have to transform 4ft into 60ft.
what do I have to multiply 4 with to get 60 ?
4 × x = 60
x = 60/4 = 15
so, the flag pole is
15×1 = 15ft tall.
