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

∠1≅∠2 by the alternate exterior angles theorem.

step-by-step explanation:

given, a ∥ b and ∠1 ≅ ∠3 .we have to prove that e ∥ f

we know that ∠1≅∠3 and that a || b because they are given. we see that by the alternate exterior angles theorem. therefore, ∠2≅∠3 by the transitive property. so, we can conclude that e || f by the converse alternate exterior angles theorem.

we have to fill the missing statement.

transitivity property states that if a = b and b = c, then a = c.

now, given ∠1≅∠3 and by transitivity property ∠2≅∠3 .

hence, to apply transitivity property one angle must be common which is not in result after applying this property which is ∠1.

the only options in which ∠1 is present are ∠1 and ∠2, ∠1 and ∠4

∠1 and ∠4 is not possible ∵ after applying transitivity we didn't get ∠4.

hence, the missing statement is ∠1≅∠2.

so, ∠1≅∠2 by the alternate exterior angles theorem.

70 years.

step-by-step explanation: