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ghari112345
03.04.2020 •
Mathematics
Triangle J K L is shown. The length of L J is 15. Angle K L J is 28 degrees and angle L J K is 110 degrees. Determine the measures of all unknown angles and side lengths of △JKL. Round side lengths to the nearest hundredth. m∠K = ° JK ≈ LK ≈
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Ответ:
In ΔJKL: m∠K = 42°, JK ≈ 10.52 units, LK ≈ 22.08 units
Given:
∠LJK = 110°
∠KLJ = 28°
Side JL = 15 units
To find: ∠JKL = m∠K
We know that the sum of all the angles of a triangle is equal to 180°
∠LJK + ∠KLJ + ∠JKL = 180°
110° + 28° + ∠JKL = 180°
∠JKL = 180° - 138°
∠JKL = 42°
To find the side we use the Sine rule:
As per Sine rule:
Where a, b and c are the side opposite to ∠A, ∠B, and ∠C respectively.
Using the Sine rule in the given triangle
Solving:
Solving:
Therefore, m∠K = 42°, JK ≈ 10.52 units LK ≈ 22.08 units
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Ответ:
∠JKL = 42°
JK = 10.52
LK = 21.07
Step-by-step explanation:
We will use sine rule to find length of unknown sides.
The sin rule is:
First, lets find the unknown angle ∠JKL.
We know sum of all 3 angles in a triangle is 180, so
28 + 110 + ∠JKL = 180
∠JKL = 180 - 28 - 110 = 42°
Now using sine rule, we find JK:
Now using sin rule, we find LK:
Ответ: