e $\\sin^{-1}$ function.\n3. Type '0.6' and press [ENTER]."},"desmos":{"expression":"\\arcsin(0.6)","instructions":"1. Click the wrench icon in the top right to open settings and ensure 'Degrees' is selected.\n2. In an input cell, type `arcsin(0.6)` or use the keypad to select `sin^-1`."},"description":"Calculate the inverse sine of 0.6 in degree mode to find the angle."}],"highlights":[{"text":"3 significant figures","location":"specification"}]}]}],"generatedAt":"2026-06-13T02:31:28.857Z","modelVersion":"gemini-3.5-flash","explanationVersion":"v2"},"firstAttemptFullMarks":null,"walkthroughVideo":{"url":"https://assets.mathsgenie.co.uk/walkthroughs/videos/b7bfb7bc-af13-4a04-b6a7-f8de34c6992e.mp4","durationSeconds":120,"posterUrl":"https://assets.mathsgenie.co.uk/walkthroughs/videos/b7bfb7bc-af13-4a04-b6a7-f8de34c6992e.jpg"}},{"id":"babfc30d-d017-4fd2-8901-712131259a60","revisionId":"bce3538e-d105-447f-987e-fe74c1e7e12f","questionNumber":null,"questionType":"LA","specification":"![A triangular decorative tile has two sides labeled x cm and (x + 6) cm, with an included angle of 45 degrees.](https://assets.mathsgenie.co.uk/question-image-redraws/sol-max-v1/babfc30d-d017-4fd2-8901-712131259a60/image-1-2c8f53e64354ee7de759b2b5.svg)","difficulty":4,"difficultyBand":"medium","totalMarks":5,"sourceTitle":null,"calculatorUse":"calc","isCalculation":true,"parts":[{"id":"fc5b46dd-3e6e-4f90-910d-121b921f0fed","label":"a","content":"The area of the tile is $20 \\text{ cm}^2$. \nWork out the value of $x$. \nGive your answer to 3 significant figures.","markscheme":"- Sets up equation: $\\frac{1}{2}(x)(x+6)\\sin(45) = 20$ M1\n- Simplifies to $x^2 + 6x = \\frac{40}{\\sin(45)}$ or $x^2 + 6x \\approx 56.568$ M1\n- Forms quadratic $x^2 + 6x - 56.568... = 0$ M1\n- Applies quadratic formula $x = \\frac{-6 \\pm \\sqrt{6^2 - 4(1)(-56.568)}}{2}$ M1\n- Calculates $x = 5.10$ A1","marks":5,"order":0,"markingRubric":{"totalMarks":5,"points":[{"id":"p1","marks":1,"description":"Sets up the area equation using 1/2 * x * (x+6) * sin(45) = 20.","code":"M"},{"id":"p2","marks":1,"description":"Expansion of brackets and division by sin(45) constant.","code":"M"},{"id":"p3","marks":1,"description":"Correct identification of quadratic coefficients for formula use.","code":"M"},{"id":"p4","marks":1,"description":"Substitution into quadratic formula or use of calculator solver.","code":"M"},{"id":"p5","marks":1,"description":"Final positive root for x given to 3 significant figures.","code":"A"}],"finalAnswers":["5.10"],"generatedAt":"2026-05-06T14:01:35.298Z","modelVersion":"gemini-3-flash-preview"},"tableImages":[],"explanation":{"methods":[{"id":"quadratic_formula","label":"Form and solve a quadratic","steps":[{"type":"hyper_latex","block":{"nodes":[{"latex":"$$A=\\dfrac{1}{2}ab\\sin C$"},{"latex":"$$20=\\dfrac{1}{2}x(x + 6)\\sin 45^\\circ$"}]},"order":0,"title":"Use the area formula","description":"For two sides and their included angle, use the triangle area formula. Substituting the given measurements and area earns the first M1."},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$20=\\dfrac{1}{2}x(x+6)\\sin 45^\\circ$"},{"latex":"$$40=x(x+6)\\color{@sky}{\\htmlData{anchor=sine_from}{\\sin 45^\\circ}}$"},{"latex":"$$x(x+6)=\\dfrac{40}{\\color{@sky}{\\htmlData{anchor=sine_to}{\\sin 45^\\circ}}}$"},{"latex":"$$x(x+6)=56.568542\\ldots$"},{"latex":"$$x^2+6x=56.568542\\ldots$"}],"connections":[{"to":"sine_to","from":"sine_from","color":"sky","label":"divide by sin 45°","style":"solid"}]},"order":1,"title":"Remove the multiplier","description":"Multiply both sides by 2, then divide by sin 45°. Reaching the expanded equation earns the second M1."},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$x^2+6x=56.568542\\ldots$"},{"latex":"$$x^2+6x-56.568542\\ldots=0$"}]},"order":2,"title":"Form the quadratic","description":"Subtract the right-hand value from both sides so that one side is zero. This standard quadratic form earns the third M1."},{"type":"hyper_latex","block":{"nodes":[

Finding the Area of Any Triangle

Question 11

Finding the Area of Any Triangle Questions

Finding the Area of Any Triangle

Question 11

Finding the Area of Any Triangle Questions