SOLUTION: In \triangle PQR, we have \angle P = 90^\circ, PQ=3, and QR = 5. Find \tan R.

Question 1210134: In \triangle PQR, we have \angle P = 90^\circ, PQ=3, and QR = 5. Find \tan R.
Found 2 solutions by CPhill, ikleyn:
Answer by CPhill(1987) (Show Source): You can put this solution on YOUR website!
Let $\triangle PQR$ be a right triangle with $\angle P = 90^\circ$. We are given that $PQ = 3$ and $QR = 5$. We want to find $\tan R$.
Since $\triangle PQR$ is a right triangle, we can use the Pythagorean theorem to find the length of $PR$.
$$PQ^2 + PR^2 = QR^2$$
$$3^2 + PR^2 = 5^2$$
$$9 + PR^2 = 25$$
$$PR^2 = 25 - 9 = 16$$
$$PR = \sqrt{16} = 4$$
Now we can find $\tan R$. Recall that in a right triangle,
$$ \tan R = \frac{\text{opposite side}}{\text{adjacent side}} = \frac{PQ}{PR} $$
We have $PQ = 3$ and $PR = 4$.
$$ \tan R = \frac{3}{4} $$
Final Answer: The final answer is $\boxed{\frac{3}{4}}$

Answer by ikleyn(52847) (Show Source): You can put this solution on YOUR website!
.

You should recognize a right angled (3,4,5)-triangle immediately.

RELATED QUESTIONS
In (triangle)PQR, m <(angle)Q=90 degrees, PQ=1, and QR=3. The value for sec <(angle)R is... (answered by Alan3354)
In (triangle)PQR, m(angle) (answered by Alan3354)
In triangle PQR: Angle P= 49 degrees Angle R= 37 degrees PR=26 cm Find QR and the... (answered by stanbon)
in triangle PQR if angle r greater than angle q then (QR=PR, PQ > PR,QR LESSTHAN PR PQ <... (answered by CubeyThePenguin)
If p + q + r =1 , pq + qr + rs = -1 and pqr = -1, find the value of p^ 3 + q^ 3 + r... (answered by lynnlo)
In triangle PQR, AB//QR, If PA = 3x - 2, PB = 5x + 2, AQ = 5, BR = 10 and QR = 42, find: (answered by mananth)
Find all unknown sides and angles of triangle PQR if ANGLE P is 42 and PQ:21 cm and... (answered by kibauu)
Triangle PQR has PQ=8cm, QR= 10cm and angle PQR is 40�. Calculate the area of triangle... (answered by stanbon)
In triangle PQR the measure of angle R is 90 degrees, the measure of angle q is 49... (answered by Alan3354)