Anyone know how to do this geometry problem? Im stuck on it and could really use some help.

Explanation:

Statement . . . . Reason

1. ∠1 ≅ ∠2, ∠J ≅ ∠K . . . . given

2. AB ≅ BA . . . . reflexive property of congruence

3. ΔABK ≅ ΔBAJ . . . . AAS congruence postulate

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The shared side is congruent with itself. Two angles are said to be congruent, and one of those is adjacent to the shared side. This is the setup for claiming AAS congruence.

Additional comment

It is a good idea to be familiar with the ways triangle congruence can be claimed. There are basically 4 of them: SSS, SAS, ASA, AAS. The special case of two sides and an angle can only be claimed in the form of HL for right triangles.

In these abbreviations, S represents a side; A represents an angle. The order is important: SAS represents the case of the angle being between the two sides, for example.

The building is approximately 39 m high.

Step-by-step explanation:

As seen in the diagram attached, a triangle can be formed between the boy, the top of the building, and the lateral distance between the boy and the building.

We can now use trigonometric laws to find the distance AC between the boy's head and the top of the building.

tan 40 = AC/37.5

AC = 37.5 X tan 40 = 31.46m

We have just obtained the distance from the boy's head to the building top.

To get the true height of the building, we have to add the height of the platform the boy is standing on to the value just found.

7.5m + 31.46m = 39m