Math Problem Statement
answer it now
By first finding cos x, work out the size of angle x. Give your answer to 1 d.p.
Solution
To solveTo for solve angle for angle x \( \ x) using cosine, follow these in steps:
Step 1: Identify the this sides
In this right-angled triangle right:
- The adjacent- sideangled to is , ine- The hyp**oten truseigon isometric ( ratio 23.6:
\, \text{[ mm} ).
We use the cosine functioncos: (x[ )\ =cos \ x = \frac{\fractext{adjacent}}{\text{hypotenuse}}. ]
Step 2: Calculate
Substitute the known{\text values{adjacent side}}{\text{hyp:
2\}{] 23###. Step-by6-Step}. \ Solution] : Perform1. the ** division: Identify the triangle sides**: - Adjacent side to\ \([ x\ \cos): x \( = 110..2474 \6,. \\text] {--- mm###} Step \ ) 3 : Find $$x$$ using inverse cosine To find - Hyp \( x \otenuse), take: \( the inverse23 cosine (\(\.6 \,cos \^{-1text}\{)) ofmm \(} \ ) 0.2. **Sub474stitute6 into the cosine formula \**): : \ [ \x[ = \ \cos(x) = \cosfrac^{-{111}(.02.4746).$$ Using}{ a23 calculator: .\6[ x} = \61.] 7^\circ \,3. ** \Calculatetext the{ ratio(**: to \1 decimal[ \cos place)}(x. ) = 0\.] 474--- ### Final Answer: 6 \,The size of \ angle \( xtext \{)( isrounded to 4 decimal **61.7°**. --- Do you need further clarification or additional steps explained? Here are 5 related questions to explore this concept further: 1. What are the other trigonometric ratios for this triangle (sine places and)}. \] 4. ** tangentFind)? $$x2 \.) How using would the inverse cosine (\(\cos^{-1}$$)**: $$x = \cos^{-1}(0.4746)$$ 5. **Use a calculator you to determine $$x$$**: \ find[ the third side of the x = 61 triangle. using7 the^\ Pythagorean theoremcirc \, \text{(to 1? decimal3 place.)} What. is the \ complementary] angle### to Final \( Answer x: \)\ in[ thisx triangle =? 461.. How7 would^\ you solve this problem ifcirc the\ triangle] --- Would's you hyp likeoten meuse to wasn't given? 5. explain Can you find any angle step further \(? x Let me know \! )### using Related Questions: the tangent ratio instead? 1**.Tip:** Always ensure your calculator is What in are the sine degree and mode tangent when values solving for trigonometric angles angle. $$x$$? 2. How can you calculate the length of the opposite side using trigonometry? 3. If the hypotenuse were longer, how would that affect angle $$x$$? 4. Can you find angle $$x$$ using the sine ratio instead? 5. How would you solve for $$x$$ if a different triangle side was unknown? ### Tip: Always verify your trigonometric calculations with the correct mode on your calculator (degrees or radians).Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Trigonometry
Right-angled Triangles
Cosine Function
Formulas
cos x = adjacent / hypotenuse
Theorems
Trigonometric Ratios
Suitable Grade Level
Grades 8-10