Consider the non-right triangle below Suppose that m∠BCA=69∘, and that x=32cm and y=49cm. What is the degree measure of ∠ABC?

Step 1 Use cosine formula x=32, y=42cm ∠BCA=69∘ ∠ABC=? cos⁡69∘⇒x2+y2−222xy 3583=322+492⋅222×32×49 3563×2×32×49= 1123⋅8418=1024+2401−22 1123⋅8418=3425−22 z2⇒3425−1123⋅8418 z2=2301⋅1582 z=47⋅9703 ∠cos⁡B=z2+x2−y222x ∠cos⁡B=(47⋅9703)2+322−4922×47⋅9703×32 Step 2 cos⁡B=2301⋅1582+1024−24013070.0992 cos⁡B⇒924.15823070.0992 cos⁡B⇒⋅3010 ∠ABC=B=cos−1(⋅3010) ∠ABC=72.4811∘

Expert Answer to "Consider the non-right triangle below Suppose that m∠BCA=69∘,..."

High School
Geometry
Trigonometry
Non-right triangles and trigonometry

peromvu

Answered question

2021-11-21

Consider the non-right triangle below

Suppose that

m ∠ B C A = 69^{\circ}

, and that

x = 32 c m

and

y = 49 c m

. What is the degree measure of

∠ A B C ?

Answer & Explanation

James Obrien

Beginner2021-11-22Added 16 answers

Step 1
Use cosine formula

$x = 32, y = 42 c m$
$∠ B C A = 69^{\circ}$
$∠ A B C = ?$
${\cos 69}^{\circ} \Rightarrow \frac{x^{2} + y^{2} - 2^{2}}{2 x y}$
$3583 = \frac{32^{2} + 49^{2} \cdot 2^{2}}{2 \times 32 \times 49}$
$3563 \times 2 \times 32 \times 49 =$
$1123 \cdot 8418 = 1024 + 2401 - 2^{2}$
$1123 \cdot 8418 = 3425 - 2^{2}$
$z^{2} \Rightarrow 3425 - 1123 \cdot 8418$
$z^{2} = 2301 \cdot 1582$
$z = 47 \cdot 9703$
$∠ \cos B = \frac{z^{2} + x^{2} - y^{2}}{22 x}$
$∠ \cos B = \frac{{(47 \cdot 9703)}^{2} + 32^{2} - 49^{2}}{2 \times 47 \cdot 9703 \times 32}$
Step 2
$\cos B = \frac{2301 \cdot 1582 + 1024 - 2401}{3070.0992}$
$\cos B \Rightarrow \frac{924.1582}{3070.0992}$
$\cos B \Rightarrow \cdot 3010$
$∠ A B C = B = \cos^{- 1} (\cdot 3010)$
$∠ A B C = {72.4811}^{\circ}$

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