Create a proportion using the lengths of similar triangles.
10.75 meters
Practice makes perfect
Bartolo wants to find a height of a tree by using a hypsometer. A hypsometer uses the properties of similar triangles to estimate a height of an object. Let's take a look at the diagram to find similar triangles.
We can see that segments DE and GH are perpendicular to the ground. This means DE and GH are parallel. Therefore, ∠ E and ∠ G are congruent angles. We also know that ∠ F and ∠ H are right angles. Now, let's recall an Angle-Angle (AA) Similarity.
Angle-Angle (AA) Similarity
If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.
By this postulate, we know that △ DEF is similar to △ FGH.
△ DEF ~ △ FGH
Recall that in similar triangles corresponding sides are proportional. With this information, we can create a proportion using the given lengths of these triangles.
15/10=x/6
Now, we will solve the above equation for x using cross multiplication.
The value of x is 9 m. However, we need to remember that the height of a tree is the value of x plus the Bartolo's height, which is 1.75 m.
9+ 1.75=10.75
The height of this tree is 10.75 meters.
