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First we need to find side b Pythagoras Theorem states: #a^2+b^2=c^2# So: #b^2=c^2-a^2# #:.# #b^2=(42)^2-(28)^2=1764-784=980=>b=sqrt(980)=14sqrt(5)# There are a few different ways of finding the remaining angles, this is just one of them. #tanA=a/b# #:.# #tanA=28/(14sqrt(5))=2/sqrt(5)=(2sqrt(5))/5# #A = tan^-1(tanA)=tan^-1((2sqrt(5))/5)=41.81^o# Angle B The sum of the angles in a triangle add up to #180^o# #:.# #180^o-(41.81^o + 90^o)=48.19^o# Full solution: #A=41.81^o# #B=48.19^o# #C=90^o# #a=28# #b=14sqrt(5)~~31.3# #c=42#
Isabella B. b=15mm, B=27 degree, C=96 degree More 2 Answers By Expert Tutors
A = 180° - 27° - 96° 15 / sin 27° = c / sin 96° a / sin A = 15 / sin 27°
Jesse G. answered • 06/05/20 3D Modeling and Math Tutoring Given: b = 15 B = 27 C = 96 Find: a, c, A To find A, we can simply subtract the two other angles (B and C) from 180: 180 - B - C = 180 - 27 - 96 = 57 To find the sides a and c we can use this identity: a/sinA = b/sinB = c/sinC a/sin(57) = 15/sin(27) a = 15*sin(57)/sin(27) a = 6.84 c/sin(96) = 15/sin(27) c = 15.43 Still looking for help? Get the right answer, fast.ORFind an Online Tutor Now Choose an expert and meet online. No packages or subscriptions, pay only for the time you need. How do you find missing sides and angles of a non-right triangle, triangle ABC, angle C is 115, side b is 5, side c is 10?Answer Verified
Hint: In this question, we have to find the rest of the missing sides and angles. We will use the sine rule to find all the missing terms as we are given two sides and one angle in this question. Complete step by step answer: So, it says that when we divide side ‘a’ by the sine of $ \angle A $ it is equal to side ‘b’ divided by the sine of $ \angle B $ and also equal to side ‘c’ divided by the sine of $ \angle C $ . $ \Rightarrow \dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C} $ Now, make a figure to see what all terms are given. According to the law of sine: $ \Rightarrow \dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C} $ As, b = 5, c = 10 and $ \angle C $ = $ {{115}^{\circ }} $ . So we have to equate $ \dfrac{b}{\sin B} $ and $ \dfrac{c}{\sin C} $ to find $ \angle B $ . $ \Rightarrow \dfrac{b}{\sin B}=\dfrac{c}{\sin C} $ Now put the values: $ \Rightarrow \dfrac{5}{\sin B}=\dfrac{10}{\sin {{115}^{\circ }}} $ Now, leave sin B alone. $ \Rightarrow 5\times \dfrac{\sin {{115}^{\circ }}}{10}=\sin B $ $ \Rightarrow \dfrac{0.9063}{2}=\sin B $ $ \Rightarrow 0.45=\sin B $ Now, use the inverse function of sine. $ \Rightarrow {{\sin }^{-1}}0.45=B $ So, B = 26.95 Now, by angle sum property of a triangle, the sum of three angles of a triangle is $ {{180}^{\circ }} $ . So, let’s apply angle sum property to find $ \angle A $ . $ \Rightarrow \angle A+\angle B+\angle C={{180}^{\circ }} $ Put the value of B = 26.95 and $ \angle C={{115}^{\circ }} $ : $ \Rightarrow \angle A+26.95+{{115}^{\circ }}={{180}^{\circ }} $ $ \Rightarrow \angle A+141.95={{180}^{\circ }} $ $ \Rightarrow \angle A={{180}^{\circ }}-141.95 $ $ \therefore \angle A=38.05 $ Now, we have to find side ‘a’. As we know: $ \Rightarrow \dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C} $ Now, let’s equate $ \dfrac{a}{\sin A} $ and $ \dfrac{c}{\sin C} $ Now, put the value c = 10, $ A=38.05 $ , C = $ {{115}^{\circ }} $ : $ \Rightarrow \dfrac{a}{\sin A}=\dfrac{c}{\sin C} $ $ \Rightarrow \dfrac{a}{\sin 38.05}=\dfrac{10}{\sin {{115}^{\circ }}} $ $ \begin{align} & \Rightarrow \dfrac{a}{0.6163}=\dfrac{10}{0.9063} \\ & \Rightarrow a=\dfrac{10}{0.9063}\times 0.6163 \\ \end{align} $ After simplifying we get: $ \therefore $ a = 6.8 So, our final answer is: a = 6.8, $ \angle B $ = 26.95, $ \angle A=38.05 $ . Note: How do you find the missing side and angle of a triangle?Given two sides. if leg a is the missing side, then transform the equation to the form when a is on one side, and take a square root: a = √(c² - b²). if leg b is unknown, then. b = √(c² - a²). for hypotenuse c missing, the formula is. c = √(a² + b²). How do you find 3 missing sides of a triangle?Different Ways to Find the Third Side of a Triangle
For a right triangle, use the Pythagorean Theorem. For an isosceles triangle, use the area formula for an isosceles. If you know some of the angles and other side lengths, use the law of cosines or the law of sines.
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