A couple of students are testing a prototype for a science project on rockets. They launch the rocket and record its height over
time. The table shows the height of the rocket in meters, f(x), and the time in seconds after launch, x. Create the function, in standard form, that models this situation.
2 answers:
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Since RT is perpendicular to the river, you have that segment CT is perpendicular to RT and, thus, CT⊥RB, because point B lies in a straight line with points R and B. Angles TCR and TCB are congruent (she walks from C in a direction that makes the same angle as TCR with the river bank on her side of the river).
This means that triangle CRB is isosceles triangle with base BR and height CT, because height CT is also a bisector of angle BCR.
The height CT divides triangle BCR into two right triangles BCT and RCT, where:
- CT is common leg;
- ∠TCR≅∠TCB,
then by LA Theorem these two triangles are congruent (ΔBCT≅ΔRCT).
Congruent triangles have congruent corresponding sides:
- BC≅RC;
- CT≅CT;
- BT≅TR.
If BT turns out to be 75 yards, then TR=75 yards.
By the Pythagorean theorem,
If then distance from the spot to the rock is
Answer: RT=75 yards, yards.
