A monument in the shape of a right triangle sits on a rectangular pedestarl that is 7 meters high by 16 meters long. The longest side of the triangular monument measure 65 meters. How high off the ground is the top of the monument

height = 63  m

Step-by-step explanation:

The shape of the monument is a triangle. The triangle is a right angle triangle. The triangular monument is sitting on a rectangular pedestal that is 7 m high and 16 m long.  The longest side of the triangular monument is 65 m . The longest side of a right angle triangle is usually the hypotenuse. The adjacent side of the triangle which is the base of the triangle sitting on the rectangular pedestal is 16 m long.

Since the triangle  formed is a right angle triangle, the height of the triangular monument can be gotten using Pythagoras's theorem.

c² = a² + b²

where

c is the hypotenuse side while side a and b is the other sides of the right angle triangle.

65² - 16² = height²

height² = 4225  - 256

height² = 3969

square root both sides

height = √3969

height = 63  m

x =-.20752

step-by-step explanation:

4^(x+2)=12

4^(x+2)=12

take the log base 4 on each side

log 4 (4^(x+2) = log 4(12)

we know log b(a^y) = y log b (a)

(x+2) log 4(4) = log 4 (12)

x+2 = log 4 (12)

we know   logb c = loga c/loga b

we want to convert to base 10   so a = 10

by default, we do not write the 10   c = 4   and b = 10

log4 10 = log 12/log 4

log4 10 = log 12/ log 4

x+2 = log 12/ log 4

subtract 2 from each side

x +2 -2 = log 12/ log 4 -2

x = 1.79248125 -2

x =-.20752