1. ## Triangle word problem

A building was to be built on a triangular piece of property. The architect was given the measurements of the angles of the triangle as 54, 39, and 87 degrees and the lengths of two of the sides as 100m and 80m. When the architect began to draw up the design on paper, she drew a triangle to scale with the corresponding measures and found that the lot was considerably smaller than she had been led to believe. It appeared that the proposed building would not fit on the property. She called the surveyor and he confirmed each of the measurements and could not see any problem with the size. Neither could understand the reason for the other's opinion. What is the reason for the miscommunication and what should be done to clear up the situation?

2. Hello, igottaquestion!

A building was to be built on a triangular piece of property.
The architect was given the angles of the triangle as 54°, 39°, and 87°
and the lengths of two of the sides as 100m and 80m.

When the architect drew a triangle to scale with the corresponding measures,
she found that the lot was considerably smaller than she had been led to believe.
It appeared that the proposed building would not fit on the property.

She called the surveyor and he confirmed each of the measurements
and could not see any problem with the size.
Neither could understand the reason for the other's opinion.

What is the reason for the miscommunication
and what should be done to clear up the situation?

He should fax her a diagram of the property.

From the given information, there are three possible triangles.

Code:
                        *
* 87°*
*         *
80 *              *
*                   *
* 39°                54° *
*  *  *  *  *  *  *  *  *  *  *
100
$\text{Area} \;\approx\;2517.28\text{ m}^2$

Code:
                        *
* 87°*
*         *
*              * 80
*                   *
* 39°                54° *
*  *  *  *  *  *  *  *  *  *  *
100
$\text{Area} \;\approx\;3236.07\text{ m}^2$

Code:
                        *
* 87°*
*         *
80 *              * 100
*                   *
* 39°                54° *
*  *  *  *  *  *  *  *  *  *  *
$\text{Area} \;\approx\;3994.52\text{ m}^2$