In triangle PQR, the side lengths are p = 8\text{ cm} and q = 15\text{ cm}, and the includ… — JAMB UTME

In triangle $PQR$ , the side lengths are $p = 8\text{ cm}$ and $q = 15\text{ cm}$ , and the included angle $\angle R = 60^\circ$ . What is the length of side $r$ in centimeters?

Cevap: 13 cm

Cevap

The length of side

r

13\text{ cm}

Using the Cosine Rule formula

r^2 = p^2 + q^2 - 2pq \cos R

with

p=8

q=15

, and

R=60^\circ

, we calculate

r^2 = 64 + 225 - 240(0.5) = 169

. Taking the square root gives

r = 13\text{ cm}

Adım Adım Çözüm

Identify the given values and appropriate trigonometric rule

Givens:

p = 8\text{ cm}

q = 15\text{ cm}

\angle R = 60^\circ

. Since two sides and the included angle (SAS) are given, use the Cosine Rule:

r^2 = p^2 + q^2 - 2pq \cos R

The Cosine Rule is required to find the third side when two sides and their included angle are known.

Substitute the values into the Cosine Rule formula

r^2 = 8^2 + 15^2 - 2(8)(15) \cos 60^\circ

Replacing variables with their numerical equivalents sets up the algebraic calculation.

Calculate the terms and evaluate

r^2

r^2 = 64 + 225 - 240 \times 0.5 = 289 - 120 = 169

Since

\cos 60^\circ = 0.5

, simplify the arithmetic operations.

Solve for side length

r

r = \sqrt{169} = 13\text{ cm}

Take the square root of both sides to obtain the length of side

r

Anahtar Kavram

Applying the Cosine Rule to find an unknown side given two sides and the included angle (SAS)

Soru

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Konular

Bu konudan daha fazla soru